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jump-dev / Pajarito.jl

A solver for mixed-integer convex optimization
Mozilla Public License 2.0
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returned NaNs - check if fixed by MPB/JuMP status rework #380

Closed joehuchette closed 6 years ago

joehuchette commented 7 years ago

Model:

using JuMP, PolyJuMP, SumOfSquares, MultivariatePolynomials, Pajarito, Gurobi, Mosek

r = 4
M = 60
N = M
O = [5:5:M;]

WIDTH = 0.6

Γ = Dict(o => rand() for o in O)
L = Dict(o => max(0,Γ[o]-WIDTH/2) for o in O)
U = Dict(o => min(1,Γ[o]+WIDTH/2) for o in O)

T = linspace(0, 1, N+1)

X₀   = 0.5
X₀′  = 0
X₀′′ = 0

model = SOSModel(solver=PajaritoSolver(mip_solver=GurobiSolver(), mip_subopt_solver=GurobiSolver(), cont_solver=MosekSolver(), mip_solver_drives=true, cut_zero_tol=1e-8))

@polyvar(t)
Z = monomials([t], 0:r)

p = Vector{Any}(N)
for j in 1:N
    p[j] = @polyvariable(model, tmp, Z)
    @polyconstraint(model, p[j] >= 0, domain = (t >= T[j] && t <= T[j+1]))
    @polyconstraint(model, p[j] <= 1, domain = (t >= T[j] && t <= T[j+1]))
end

@variable(model, H[O], Bin)
for o in O
    γ = rand()
    l = L[o]
    u = U[o]
    @polyconstraint(model, p[o] >= u*   H[o] , domain = (t >= T[o] && t <= T[o+1]))
    @polyconstraint(model, p[o] <= l*(1-H[o]), domain = (t >= T[o] && t <= T[o+1]))
end

@constraint(model, p[1]([0], [t]) == X₀)
@constraint(model, differentiate(p[1], t)([0], [t]) == X₀′)
@constraint(model, differentiate(differentiate(p[1], t), t)([0], [t]) == X₀′′)

for j in 1:N-1
    @constraint(model, p[j]([T[j+1]], [t]) == p[j+1]([T[j+1]], [t]))
    @constraint(model, differentiate(p[j], t)([T[j+1]], [t]) == differentiate(p[j+1], t)([T[j+1]], [t]))
    @constraint(model, differentiate(differentiate(p[j], t), t)([T[j+1]], [t]) == differentiate(differentiate(p[j+1], t), t)([T[j+1]], [t]))
end

solve(model)

Output:

Problem
  Name                   :
  Objective sense        : min
  Type                   : CONIC (conic optimization problem)
  Constraints            : 7104
  Cones                  : 0
  Scalar variables       : 5496
  Matrix variables       : 864
  Integer variables      : 0

Optimizer started.
Conic interior-point optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 1730
Eliminator terminated.
Eliminator started.
Freed constraints in eliminator : 0
Eliminator terminated.
Eliminator - tries                  : 2                 time                   : 0.00
Lin. dep.  - tries                  : 1                 time                   : 0.00
Lin. dep.  - number                 : 0
Presolve terminated. Time: 0.01
Optimizer  - threads                : 4
Optimizer  - solved problem         : the primal
Optimizer  - Constraints            : 5359
Optimizer  - Cones                  : 1
Optimizer  - Scalar variables       : 3764              conic                  : 3740
Optimizer  - Semi-definite variables: 864               scalarized             : 5184
Factor     - setup time             : 0.02              dense det. time        : 0.00
Factor     - ML order time          : 0.00              GP order time          : 0.00
Factor     - nonzeros before factor : 4.10e+04          after factor           : 5.65e+04
Factor     - dense dim.             : 2                 flops                  : 9.77e+05
ITE PFEAS    DFEAS    GFEAS    PRSTATUS   POBJ              DOBJ              MU       TIME
0   1.0e+00  1.0e+00  1.0e+00  0.00e+00   0.000000000e+00   0.000000000e+00   1.0e+00  0.06
1   7.7e-01  7.7e-01  8.9e-01  1.82e+00   0.000000000e+00   5.162426755e-02   7.7e-01  0.14
2   4.3e-01  4.3e-01  5.8e-01  2.02e+00   0.000000000e+00   2.122528514e-01   4.3e-01  0.20
3   3.4e-01  3.4e-01  2.8e-01  -3.77e-01  0.000000000e+00   8.726151275e-01   3.4e-01  0.27
4   5.0e-02  5.0e-02  1.5e-02  -1.10e-01  0.000000000e+00   1.043725295e+01   5.0e-02  0.34
5   1.5e-02  1.5e-02  4.9e-03  -1.42e-01  0.000000000e+00   9.276464801e+00   1.5e-02  0.41
6   8.1e-03  8.1e-03  3.4e-03  2.33e-01   0.000000000e+00   5.432059719e+00   8.1e-03  0.48
7   2.9e-03  2.9e-03  2.1e-03  5.50e-01   0.000000000e+00   1.864126642e+00   2.9e-03  0.55
8   1.4e-03  1.4e-03  1.4e-03  8.02e-01   0.000000000e+00   1.002368716e+00   1.4e-03  0.62
9   8.1e-04  8.1e-04  1.0e-03  8.17e-01   0.000000000e+00   6.403814357e-01   8.1e-04  0.70
10  2.8e-04  2.8e-04  5.2e-04  8.31e-01   0.000000000e+00   2.671022584e-01   2.8e-04  0.76
11  1.4e-04  1.4e-04  3.4e-04  8.15e-01   0.000000000e+00   1.533668066e-01   1.4e-04  0.82
12  9.0e-05  9.0e-05  2.6e-04  7.90e-01   0.000000000e+00   1.181807208e-01   9.0e-05  0.89
13  4.4e-05  4.4e-05  1.6e-04  7.32e-01   0.000000000e+00   7.435566109e-02   4.4e-05  0.96
14  2.9e-05  2.9e-05  1.3e-04  7.97e-01   0.000000000e+00   4.985962781e-02   2.9e-05  1.03
15  8.9e-06  8.9e-06  6.7e-05  8.52e-01   0.000000000e+00   1.732119960e-02   8.9e-06  1.10
16  2.7e-06  2.7e-06  3.7e-05  9.53e-01   0.000000000e+00   5.433832571e-03   2.7e-06  1.16
17  6.3e-07  6.0e-07  1.7e-05  9.92e-01   0.000000000e+00   1.250816423e-03   6.0e-07  1.24
18  1.3e-07  9.9e-08  6.8e-06  1.00e+00   0.000000000e+00   2.074794361e-04   9.9e-08  1.32
19  3.9e-08  2.0e-08  3.0e-06  1.00e+00   0.000000000e+00   4.171160093e-05   2.0e-08  1.40
20  6.8e-09  3.6e-09  1.3e-06  1.00e+00   0.000000000e+00   7.391383733e-06   3.5e-09  1.55
21  1.2e-09  6.9e-10  5.4e-07  1.00e+00   0.000000000e+00   1.326597698e-06   6.2e-10  1.68
22  1.2e-09  6.6e-10  5.3e-07  1.00e+00   0.000000000e+00   1.260546736e-06   5.9e-10  1.94
23  1.2e-09  6.6e-10  5.3e-07  1.00e+00   0.000000000e+00   1.260546736e-06   5.9e-10  2.49
Interior-point optimizer terminated. Time: 3.04.

Optimizer terminated. Time: 3.04

Interior-point solution summary
  Problem status  : PRIMAL_AND_DUAL_FEASIBLE
  Solution status : NEAR_OPTIMAL
  Primal.  obj: 0.0000000000e+00    nrm: 1e+03    Viol.  con: 1e-07    var: 0e+00    barvar: 0e+00
  Dual.    obj: 1.2605467357e-06    nrm: 1e+03    Viol.  con: 2e-08    var: 8e-09    barvar: 3e-08
WARNING: Conic solver failure on initial relaxation: returned status Stall
Optimize a model with 9696 rows, 5496 columns and 29675 nonzeros
Variable types: 5484 continuous, 12 integer (12 binary)
Coefficient statistics:
  Matrix range     [8e-08, 1e+01]
  Objective range  [0e+00, 0e+00]
  Bounds range     [0e+00, 0e+00]
  RHS range        [2e-02, 1e+00]
Presolve removed 2909 rows and 299 columns
Presolve time: 0.01s
Presolved: 6787 rows, 5197 columns, 25801 nonzeros
Variable types: 5185 continuous, 12 integer (12 binary)

Root relaxation: objective 0.000000e+00, 3031 iterations, 0.24 seconds
Problem
  Name                   :
  Objective sense        : min
  Type                   : CONIC (conic optimization problem)
  Constraints            : 7092
  Cones                  : 0
  Scalar variables       : 5484
  Matrix variables       : 864
  Integer variables      : 0

Optimizer started.
Conic interior-point optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 1730
Eliminator terminated.
Eliminator started.
Freed constraints in eliminator : 0
Eliminator terminated.
Eliminator - tries                  : 2                 time                   : 0.00
Lin. dep.  - tries                  : 1                 time                   : 0.00
Lin. dep.  - number                 : 0
Presolve terminated. Time: 0.01
Optimizer  - threads                : 4
Optimizer  - solved problem         : the primal
Optimizer  - Constraints            : 5359
Optimizer  - Cones                  : 1
Optimizer  - Scalar variables       : 3752              conic                  : 3740
Optimizer  - Semi-definite variables: 864               scalarized             : 5184
Factor     - setup time             : 0.02              dense det. time        : 0.00
Factor     - ML order time          : 0.01              GP order time          : 0.00
Factor     - nonzeros before factor : 4.10e+04          after factor           : 5.65e+04
Factor     - dense dim.             : 2                 flops                  : 9.77e+05
ITE PFEAS    DFEAS    GFEAS    PRSTATUS   POBJ              DOBJ              MU       TIME
0   1.0e+00  1.0e+00  1.0e+00  0.00e+00   0.000000000e+00   0.000000000e+00   1.0e+00  0.08
1   7.7e-01  7.7e-01  8.7e-01  2.08e+00   0.000000000e+00   9.817426029e-02   7.7e-01  0.16
2   4.5e-01  4.5e-01  5.6e-01  2.21e+00   0.000000000e+00   2.835099536e-01   4.5e-01  0.22
3   3.1e-01  3.1e-01  1.7e-01  -4.07e-01  0.000000000e+00   2.408784953e+00   3.1e-01  0.28
4   8.5e-02  8.5e-02  3.1e-02  2.38e-01   0.000000000e+00   6.782154949e+00   8.5e-02  0.36
5   2.2e-02  2.2e-02  7.8e-03  -3.75e-01  0.000000000e+00   7.650579911e+00   2.2e-02  0.42
6   1.3e-02  1.3e-02  5.2e-03  -2.16e-01  0.000000000e+00   6.180762352e+00   1.3e-02  0.48
7   7.2e-03  7.2e-03  3.6e-03  1.60e-01   0.000000000e+00   3.852387177e+00   7.2e-03  0.55
8   3.4e-03  3.4e-03  2.2e-03  4.83e-01   0.000000000e+00   2.183484764e+00   3.4e-03  0.62
9   1.2e-03  1.2e-03  1.2e-03  5.92e-01   0.000000000e+00   8.834949264e-01   1.2e-03  0.68
10  6.4e-04  6.4e-04  8.7e-04  8.24e-01   0.000000000e+00   5.179695823e-01   6.4e-04  0.75
11  3.2e-04  3.2e-04  5.8e-04  8.48e-01   0.000000000e+00   2.942344716e-01   3.2e-04  0.82
12  1.6e-04  1.6e-04  3.9e-04  8.42e-01   0.000000000e+00   1.601736349e-01   1.6e-04  0.88
13  6.6e-05  6.6e-05  2.3e-04  8.76e-01   0.000000000e+00   8.188877771e-02   6.6e-05  0.96
14  3.3e-05  3.3e-05  1.5e-04  7.84e-01   0.000000000e+00   4.487005438e-02   3.3e-05  1.01
15  1.9e-05  1.9e-05  1.2e-04  8.71e-01   0.000000000e+00   2.744132012e-02   1.9e-05  1.08
16  6.8e-06  6.8e-06  6.7e-05  9.23e-01   0.000000000e+00   1.021098843e-02   6.8e-06  1.15
17  2.3e-06  2.3e-06  3.8e-05  9.85e-01   0.000000000e+00   3.423811429e-03   2.3e-06  1.22
18  4.0e-07  3.9e-07  1.6e-05  9.96e-01   0.000000000e+00   6.055082514e-04   3.9e-07  1.28
19  9.8e-08  7.5e-08  6.8e-06  9.99e-01   0.000000000e+00   1.172050822e-04   7.5e-08  1.36
20  4.0e-08  1.8e-08  3.1e-06  1.00e+00   0.000000000e+00   2.379364530e-05   1.5e-08  1.42
21  1.9e-08  4.1e-09  1.5e-06  1.00e+00   0.000000000e+00   5.363435609e-06   3.4e-09  1.49
22  5.1e-09  1.0e-09  7.4e-07  1.00e+00   0.000000000e+00   1.379608167e-06   8.7e-10  1.62
23  1.6e-09  4.6e-10  4.2e-07  1.00e+00   0.000000000e+00   4.435858331e-07   2.8e-10  1.75
24  1.6e-09  4.6e-10  4.2e-07  1.00e+00   0.000000000e+00   4.435858331e-07   2.8e-10  2.30
Interior-point optimizer terminated. Time: 2.85.

Optimizer terminated. Time: 2.85

Interior-point solution summary
  Problem status  : PRIMAL_AND_DUAL_FEASIBLE
  Solution status : NEAR_OPTIMAL
  Primal.  obj: 0.0000000000e+00    nrm: 1e+03    Viol.  con: 1e-07    var: 0e+00    barvar: 0e+00
  Dual.    obj: 4.4358583313e-07    nrm: 1e+03    Viol.  con: 0e+00    var: 3e-09    barvar: 2e-08
Total elapsed time = 5.53s
Optimizer started.
Conic interior-point optimizer started.
Presolve started.
Presolve terminated. Time: 0.01
0   1.5e+00  1.0e+00  1.0e+00  0.00e+00   0.000000000e+00   0.000000000e+00   1.0e+00  0.07
1   1.2e+00  7.7e-01  8.8e-01  2.08e+00   0.000000000e+00   9.686900451e-02   7.7e-01  0.12
2   6.7e-01  4.5e-01  5.6e-01  2.21e+00   0.000000000e+00   2.835332909e-01   4.5e-01  0.19
3   4.7e-01  3.1e-01  1.7e-01  -4.11e-01  0.000000000e+00   2.480070915e+00   3.1e-01  0.27
4   1.3e-01  8.5e-02  3.1e-02  2.46e-01   0.000000000e+00   6.892231397e+00   8.5e-02  0.32
5   3.3e-02  2.2e-02  7.8e-03  -3.67e-01  0.000000000e+00   7.656613217e+00   2.2e-02  0.39
6   2.0e-02  1.3e-02  5.0e-03  -2.36e-01  0.000000000e+00   6.435712946e+00   1.3e-02  0.46
7   1.3e-02  8.5e-03  3.3e-03  -1.86e-02  0.000000000e+00   6.380253179e+00   8.5e-03  0.49
8   5.7e-03  3.8e-03  9.2e-04  -7.78e-01  0.000000000e+00   1.687257722e+01   3.8e-03  0.56
9   2.1e-03  1.4e-03  2.3e-04  -7.44e-01  0.000000000e+00   3.569362337e+01   1.4e-03  0.58
10  4.2e-04  2.8e-04  2.3e-05  -9.00e-01  0.000000000e+00   1.539421755e+02   2.8e-04  0.65
11  6.8e-05  4.5e-05  1.5e-06  -9.86e-01  0.000000000e+00   9.301738914e+02   4.5e-05  0.72
12  1.5e-05  9.4e-06  1.4e-07  -9.97e-01  0.000000000e+00   4.399621146e+03   9.4e-06  0.78
13  8.6e-06  2.2e-06  1.6e-08  -9.95e-01  0.000000000e+00   1.843118218e+04   2.2e-06  0.85
14  5.4e-06  3.7e-07  1.3e-09  -9.41e-01  0.000000000e+00   8.417342274e+04   3.9e-07  0.93
15  3.3e-06  7.2e-08  1.4e-10  -7.30e-01  0.000000000e+00   2.633466394e+05   8.0e-08  1.00
16  5.3e-07  1.5e-08  1.1e-11  -7.94e-01  0.000000000e+00   1.224713582e+06   1.4e-08  1.08
17  2.4e-07  3.1e-09  1.1e-12  -9.82e-01  0.000000000e+00   6.082287381e+06   2.9e-09  1.15
18  7.6e-08  1.6e-09  1.2e-13  -9.85e-01  0.000000000e+00   2.682774392e+07   6.7e-10  1.28
19  7.6e-08  1.6e-09  1.2e-13  -9.91e-01  0.000000000e+00   2.682774392e+07   6.7e-10  1.83
Interior-point optimizer terminated. Time: 2.37.

Optimizer terminated. Time: 2.37

Interior-point solution summary
  Problem status  : PRIMAL_INFEASIBLE
  Solution status : NEAR_PRIMAL_INFEASIBLE_CER
  Dual.    obj: 1.3546392279e-01    nrm: 2e+02    Viol.  con: 0e+00    var: 3e-11    barvar: 2e-09
Total elapsed time = 14.36s
Total elapsed time = 16.33s
Optimizer started.
Conic interior-point optimizer started.
Presolve started.
Presolve terminated. Time: 0.01
0   1.0e+00  1.0e+00  1.0e+00  0.00e+00   0.000000000e+00   0.000000000e+00   1.0e+00  0.06
1   7.7e-01  7.7e-01  8.7e-01  2.08e+00   0.000000000e+00   9.817426029e-02   7.7e-01  0.13
2   4.5e-01  4.5e-01  5.6e-01  2.21e+00   0.000000000e+00   2.835099536e-01   4.5e-01  0.20
3   3.1e-01  3.1e-01  1.7e-01  -4.07e-01  0.000000000e+00   2.408784953e+00   3.1e-01  0.27
4   8.5e-02  8.5e-02  3.1e-02  2.38e-01   0.000000000e+00   6.782154952e+00   8.5e-02  0.33
5   2.2e-02  2.2e-02  7.8e-03  -3.75e-01  0.000000000e+00   7.650579901e+00   2.2e-02  0.40
6   1.3e-02  1.3e-02  5.2e-03  -2.16e-01  0.000000000e+00   6.180762331e+00   1.3e-02  0.46
7   7.2e-03  7.2e-03  3.6e-03  1.60e-01   0.000000000e+00   3.852387067e+00   7.2e-03  0.52
8   3.4e-03  3.4e-03  2.2e-03  4.83e-01   0.000000000e+00   2.183484698e+00   3.4e-03  0.59
9   1.2e-03  1.2e-03  1.2e-03  5.92e-01   0.000000000e+00   8.834949954e-01   1.2e-03  0.66
10  6.4e-04  6.4e-04  8.7e-04  8.24e-01   0.000000000e+00   5.179695844e-01   6.4e-04  0.72
11  3.2e-04  3.2e-04  5.8e-04  8.48e-01   0.000000000e+00   2.942348279e-01   3.2e-04  0.78
12  1.6e-04  1.6e-04  3.9e-04  8.42e-01   0.000000000e+00   1.601741221e-01   1.6e-04  0.85
13  6.6e-05  6.6e-05  2.3e-04  8.76e-01   0.000000000e+00   8.188838054e-02   6.6e-05  0.91
14  3.3e-05  3.3e-05  1.5e-04  7.84e-01   0.000000000e+00   4.486984484e-02   3.3e-05  0.98
15  1.9e-05  1.9e-05  1.2e-04  8.71e-01   0.000000000e+00   2.743815587e-02   1.9e-05  1.05
16  6.8e-06  6.8e-06  6.7e-05  9.23e-01   0.000000000e+00   1.021228635e-02   6.8e-06  1.11
17  2.3e-06  2.3e-06  3.8e-05  9.85e-01   0.000000000e+00   3.429048443e-03   2.3e-06  1.18
18  4.1e-07  3.9e-07  1.6e-05  9.96e-01   0.000000000e+00   6.074272240e-04   3.9e-07  1.25
19  9.9e-08  7.6e-08  6.9e-06  9.99e-01   0.000000000e+00   1.179217346e-04   7.6e-08  1.34
20  3.3e-08  1.6e-08  3.1e-06  1.00e+00   0.000000000e+00   2.392671668e-05   1.5e-08  1.40
21  7.2e-09  3.5e-09  1.5e-06  1.00e+00   0.000000000e+00   5.372004494e-06   3.4e-09  1.53
22  1.8e-09  9.1e-10  7.4e-07  1.00e+00   0.000000000e+00   1.374818621e-06   8.7e-10  1.66
23  1.4e-09  3.4e-10  4.2e-07  1.00e+00   0.000000000e+00   4.355338963e-07   2.8e-10  1.78
24  1.4e-09  3.4e-10  4.2e-07  1.00e+00   0.000000000e+00   4.355338963e-07   2.8e-10  2.34
Interior-point optimizer terminated. Time: 2.89.

Optimizer terminated. Time: 2.89

Interior-point solution summary
  Problem status  : PRIMAL_AND_DUAL_FEASIBLE
  Solution status : NEAR_OPTIMAL
  Primal.  obj: 0.0000000000e+00    nrm: 1e+03    Viol.  con: 7e-08    var: 0e+00    barvar: 0e+00
  Dual.    obj: 4.3553389633e-07    nrm: 1e+03    Viol.  con: 0e+00    var: 3e-09    barvar: 1e-08
Optimizer started.
Conic interior-point optimizer started.
Presolve started.
Presolve terminated. Time: 0.01
0   1.0e+00  1.0e+00  1.0e+00  0.00e+00   0.000000000e+00   0.000000000e+00   1.0e+00  0.06
1   7.7e-01  7.7e-01  8.7e-01  2.08e+00   0.000000000e+00   9.817426029e-02   7.7e-01  0.13
2   4.5e-01  4.5e-01  5.6e-01  2.21e+00   0.000000000e+00   2.835099536e-01   4.5e-01  0.19
3   3.1e-01  3.1e-01  1.7e-01  -4.07e-01  0.000000000e+00   2.408784953e+00   3.1e-01  0.26
4   8.5e-02  8.5e-02  3.1e-02  2.38e-01   0.000000000e+00   6.782154949e+00   8.5e-02  0.33
5   2.2e-02  2.2e-02  7.8e-03  -3.75e-01  0.000000000e+00   7.650579911e+00   2.2e-02  0.39
6   1.3e-02  1.3e-02  5.2e-03  -2.16e-01  0.000000000e+00   6.180762352e+00   1.3e-02  0.45
7   7.2e-03  7.2e-03  3.6e-03  1.60e-01   0.000000000e+00   3.852387177e+00   7.2e-03  0.52
8   3.4e-03  3.4e-03  2.2e-03  4.83e-01   0.000000000e+00   2.183484764e+00   3.4e-03  0.58
9   1.2e-03  1.2e-03  1.2e-03  5.92e-01   0.000000000e+00   8.834949264e-01   1.2e-03  0.65
10  6.4e-04  6.4e-04  8.7e-04  8.24e-01   0.000000000e+00   5.179695823e-01   6.4e-04  0.72
11  3.2e-04  3.2e-04  5.8e-04  8.48e-01   0.000000000e+00   2.942344716e-01   3.2e-04  0.79
12  1.6e-04  1.6e-04  3.9e-04  8.42e-01   0.000000000e+00   1.601736349e-01   1.6e-04  0.85
13  6.6e-05  6.6e-05  2.3e-04  8.76e-01   0.000000000e+00   8.188877771e-02   6.6e-05  0.91
14  3.3e-05  3.3e-05  1.5e-04  7.84e-01   0.000000000e+00   4.487005438e-02   3.3e-05  0.98
15  1.9e-05  1.9e-05  1.2e-04  8.71e-01   0.000000000e+00   2.744132012e-02   1.9e-05  1.04
16  6.8e-06  6.8e-06  6.7e-05  9.23e-01   0.000000000e+00   1.021098843e-02   6.8e-06  1.11
17  2.3e-06  2.3e-06  3.8e-05  9.85e-01   0.000000000e+00   3.423811429e-03   2.3e-06  1.18
18  4.0e-07  3.9e-07  1.6e-05  9.96e-01   0.000000000e+00   6.055082514e-04   3.9e-07  1.23
19  9.8e-08  7.5e-08  6.8e-06  9.99e-01   0.000000000e+00   1.172050822e-04   7.5e-08  1.32
20  4.0e-08  1.8e-08  3.1e-06  1.00e+00   0.000000000e+00   2.379364530e-05   1.5e-08  1.39
21  1.9e-08  4.1e-09  1.5e-06  1.00e+00   0.000000000e+00   5.363435609e-06   3.4e-09  1.45
22  5.1e-09  1.0e-09  7.4e-07  1.00e+00   0.000000000e+00   1.379608167e-06   8.7e-10  1.58
23  1.6e-09  4.6e-10  4.2e-07  1.00e+00   0.000000000e+00   4.435858331e-07   2.8e-10  1.71
24  1.6e-09  4.6e-10  4.2e-07  1.00e+00   0.000000000e+00   4.435858331e-07   2.8e-10  2.26
Interior-point optimizer terminated. Time: 2.81.

Optimizer terminated. Time: 2.81

Interior-point solution summary
  Problem status  : PRIMAL_AND_DUAL_FEASIBLE
  Solution status : NEAR_OPTIMAL
  Primal.  obj: 0.0000000000e+00    nrm: 1e+03    Viol.  con: 1e-07    var: 0e+00    barvar: 0e+00
  Dual.    obj: 4.4358583313e-07    nrm: 1e+03    Viol.  con: 0e+00    var: 3e-09    barvar: 2e-08
Total elapsed time = 25.20s

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0       0.0000000    0.00000      -     -   29s

Cutting planes:
  Lazy constraints: 512

Explored 0 nodes (41442 simplex iterations) in 29.34 seconds
Thread count was 4 (of 4 available processors)

Solution count 1: 0
Pool objective bound 0

Optimal solution found (tolerance 1.00e-04)
Best objective 0.000000000000e+00, best bound 0.000000000000e+00, gap -

MIP-solver-driven algorithm summary:
 - Status               =        Optimal
 - Best feasible        =           +Inf
 - Best bound           =  +0.000000e+00
 - Relative opt. gap    =            NaN
 - Total time (s)       =       3.25e+01

So the status is optimal, but the optimal solution is a vector of NaNs.

chriscoey commented 7 years ago

Hmm thanks for this. Are you on master or not?

On May 9, 2017 6:11 PM, "Joey Huchette" notifications@github.com wrote:

Model:

using JuMP, PolyJuMP, SumOfSquares, MultivariatePolynomials, Pajarito, Gurobi, Mosek

r = 4 M = 60 N = M O = [5:5:M;]

WIDTH = 0.6

Γ = Dict(o => rand() for o in O) L = Dict(o => max(0,Γ[o]-WIDTH/2) for o in O) U = Dict(o => min(1,Γ[o]+WIDTH/2) for o in O)

T = linspace(0, 1, N+1)

X₀ = 0.5 X₀′ = 0 X₀′′ = 0

model = SOSModel(solver=PajaritoSolver(mip_solver=GurobiSolver(), mip_subopt_solver=GurobiSolver(), cont_solver=MosekSolver(), mip_solver_drives=true, cut_zero_tol=1e-8))

@polyvar(t) Z = monomials([t], 0:r)

p = Vector{Any}(N) for j in 1:N p[j] = @polyvariable(model, tmp, Z) @polyconstraint(model, p[j] >= 0, domain = (t >= T[j] && t <= T[j+1])) @polyconstraint(model, p[j] <= 1, domain = (t >= T[j] && t <= T[j+1])) end

@variable(model, H[O], Bin) for o in O γ = rand() l = L[o] u = U[o] @polyconstraint(model, p[o] >= u H[o] , domain = (t >= T[o] && t <= T[o+1])) @polyconstraint(model, p[o] <= l(1-H[o]), domain = (t >= T[o] && t <= T[o+1])) end

@constraint(model, p[1]([0], [t]) == X₀) @constraint(model, differentiate(p[1], t)([0], [t]) == X₀′) @constraint(model, differentiate(differentiate(p[1], t), t)([0], [t]) == X₀′′)

for j in 1:N-1 @constraint(model, p[j]([T[j+1]], [t]) == p[j+1]([T[j+1]], [t])) @constraint(model, differentiate(p[j], t)([T[j+1]], [t]) == differentiate(p[j+1], t)([T[j+1]], [t])) @constraint(model, differentiate(differentiate(p[j], t), t)([T[j+1]], [t]) == differentiate(differentiate(p[j+1], t), t)([T[j+1]], [t])) end

solve(model)

Output:

Problem Name : Objective sense : min Type : CONIC (conic optimization problem) Constraints : 7104 Cones : 0 Scalar variables : 5496 Matrix variables : 864 Integer variables : 0

Optimizer started. Conic interior-point optimizer started. Presolve started. Linear dependency checker started. Linear dependency checker terminated. Eliminator started. Freed constraints in eliminator : 1730 Eliminator terminated. Eliminator started. Freed constraints in eliminator : 0 Eliminator terminated. Eliminator - tries : 2 time : 0.00 Lin. dep. - tries : 1 time : 0.00 Lin. dep. - number : 0 Presolve terminated. Time: 0.01 Optimizer - threads : 4 Optimizer - solved problem : the primal Optimizer - Constraints : 5359 Optimizer - Cones : 1 Optimizer - Scalar variables : 3764 conic : 3740 Optimizer - Semi-definite variables: 864 scalarized : 5184 Factor - setup time : 0.02 dense det. time : 0.00 Factor - ML order time : 0.00 GP order time : 0.00 Factor - nonzeros before factor : 4.10e+04 after factor : 5.65e+04 Factor - dense dim. : 2 flops : 9.77e+05 ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME 0 1.0e+00 1.0e+00 1.0e+00 0.00e+00 0.000000000e+00 0.000000000e+00 1.0e+00 0.06 1 7.7e-01 7.7e-01 8.9e-01 1.82e+00 0.000000000e+00 5.162426755e-02 7.7e-01 0.14 2 4.3e-01 4.3e-01 5.8e-01 2.02e+00 0.000000000e+00 2.122528514e-01 4.3e-01 0.20 3 3.4e-01 3.4e-01 2.8e-01 -3.77e-01 0.000000000e+00 8.726151275e-01 3.4e-01 0.27 4 5.0e-02 5.0e-02 1.5e-02 -1.10e-01 0.000000000e+00 1.043725295e+01 5.0e-02 0.34 5 1.5e-02 1.5e-02 4.9e-03 -1.42e-01 0.000000000e+00 9.276464801e+00 1.5e-02 0.41 6 8.1e-03 8.1e-03 3.4e-03 2.33e-01 0.000000000e+00 5.432059719e+00 8.1e-03 0.48 7 2.9e-03 2.9e-03 2.1e-03 5.50e-01 0.000000000e+00 1.864126642e+00 2.9e-03 0.55 8 1.4e-03 1.4e-03 1.4e-03 8.02e-01 0.000000000e+00 1.002368716e+00 1.4e-03 0.62 9 8.1e-04 8.1e-04 1.0e-03 8.17e-01 0.000000000e+00 6.403814357e-01 8.1e-04 0.70 10 2.8e-04 2.8e-04 5.2e-04 8.31e-01 0.000000000e+00 2.671022584e-01 2.8e-04 0.76 11 1.4e-04 1.4e-04 3.4e-04 8.15e-01 0.000000000e+00 1.533668066e-01 1.4e-04 0.82 12 9.0e-05 9.0e-05 2.6e-04 7.90e-01 0.000000000e+00 1.181807208e-01 9.0e-05 0.89 13 4.4e-05 4.4e-05 1.6e-04 7.32e-01 0.000000000e+00 7.435566109e-02 4.4e-05 0.96 14 2.9e-05 2.9e-05 1.3e-04 7.97e-01 0.000000000e+00 4.985962781e-02 2.9e-05 1.03 15 8.9e-06 8.9e-06 6.7e-05 8.52e-01 0.000000000e+00 1.732119960e-02 8.9e-06 1.10 16 2.7e-06 2.7e-06 3.7e-05 9.53e-01 0.000000000e+00 5.433832571e-03 2.7e-06 1.16 17 6.3e-07 6.0e-07 1.7e-05 9.92e-01 0.000000000e+00 1.250816423e-03 6.0e-07 1.24 18 1.3e-07 9.9e-08 6.8e-06 1.00e+00 0.000000000e+00 2.074794361e-04 9.9e-08 1.32 19 3.9e-08 2.0e-08 3.0e-06 1.00e+00 0.000000000e+00 4.171160093e-05 2.0e-08 1.40 20 6.8e-09 3.6e-09 1.3e-06 1.00e+00 0.000000000e+00 7.391383733e-06 3.5e-09 1.55 21 1.2e-09 6.9e-10 5.4e-07 1.00e+00 0.000000000e+00 1.326597698e-06 6.2e-10 1.68 22 1.2e-09 6.6e-10 5.3e-07 1.00e+00 0.000000000e+00 1.260546736e-06 5.9e-10 1.94 23 1.2e-09 6.6e-10 5.3e-07 1.00e+00 0.000000000e+00 1.260546736e-06 5.9e-10 2.49 Interior-point optimizer terminated. Time: 3.04.

Optimizer terminated. Time: 3.04

Interior-point solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : NEAR_OPTIMAL Primal. obj: 0.0000000000e+00 nrm: 1e+03 Viol. con: 1e-07 var: 0e+00 barvar: 0e+00 Dual. obj: 1.2605467357e-06 nrm: 1e+03 Viol. con: 2e-08 var: 8e-09 barvar: 3e-08 WARNING: Conic solver failure on initial relaxation: returned status Stall Optimize a model with 9696 rows, 5496 columns and 29675 nonzeros Variable types: 5484 continuous, 12 integer (12 binary) Coefficient statistics: Matrix range [8e-08, 1e+01] Objective range [0e+00, 0e+00] Bounds range [0e+00, 0e+00] RHS range [2e-02, 1e+00] Presolve removed 2909 rows and 299 columns Presolve time: 0.01s Presolved: 6787 rows, 5197 columns, 25801 nonzeros Variable types: 5185 continuous, 12 integer (12 binary)

Root relaxation: objective 0.000000e+00, 3031 iterations, 0.24 seconds Problem Name : Objective sense : min Type : CONIC (conic optimization problem) Constraints : 7092 Cones : 0 Scalar variables : 5484 Matrix variables : 864 Integer variables : 0

Optimizer started. Conic interior-point optimizer started. Presolve started. Linear dependency checker started. Linear dependency checker terminated. Eliminator started. Freed constraints in eliminator : 1730 Eliminator terminated. Eliminator started. Freed constraints in eliminator : 0 Eliminator terminated. Eliminator - tries : 2 time : 0.00 Lin. dep. - tries : 1 time : 0.00 Lin. dep. - number : 0 Presolve terminated. Time: 0.01 Optimizer - threads : 4 Optimizer - solved problem : the primal Optimizer - Constraints : 5359 Optimizer - Cones : 1 Optimizer - Scalar variables : 3752 conic : 3740 Optimizer - Semi-definite variables: 864 scalarized : 5184 Factor - setup time : 0.02 dense det. time : 0.00 Factor - ML order time : 0.01 GP order time : 0.00 Factor - nonzeros before factor : 4.10e+04 after factor : 5.65e+04 Factor - dense dim. : 2 flops : 9.77e+05 ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME 0 1.0e+00 1.0e+00 1.0e+00 0.00e+00 0.000000000e+00 0.000000000e+00 1.0e+00 0.08 1 7.7e-01 7.7e-01 8.7e-01 2.08e+00 0.000000000e+00 9.817426029e-02 7.7e-01 0.16 2 4.5e-01 4.5e-01 5.6e-01 2.21e+00 0.000000000e+00 2.835099536e-01 4.5e-01 0.22 3 3.1e-01 3.1e-01 1.7e-01 -4.07e-01 0.000000000e+00 2.408784953e+00 3.1e-01 0.28 4 8.5e-02 8.5e-02 3.1e-02 2.38e-01 0.000000000e+00 6.782154949e+00 8.5e-02 0.36 5 2.2e-02 2.2e-02 7.8e-03 -3.75e-01 0.000000000e+00 7.650579911e+00 2.2e-02 0.42 6 1.3e-02 1.3e-02 5.2e-03 -2.16e-01 0.000000000e+00 6.180762352e+00 1.3e-02 0.48 7 7.2e-03 7.2e-03 3.6e-03 1.60e-01 0.000000000e+00 3.852387177e+00 7.2e-03 0.55 8 3.4e-03 3.4e-03 2.2e-03 4.83e-01 0.000000000e+00 2.183484764e+00 3.4e-03 0.62 9 1.2e-03 1.2e-03 1.2e-03 5.92e-01 0.000000000e+00 8.834949264e-01 1.2e-03 0.68 10 6.4e-04 6.4e-04 8.7e-04 8.24e-01 0.000000000e+00 5.179695823e-01 6.4e-04 0.75 11 3.2e-04 3.2e-04 5.8e-04 8.48e-01 0.000000000e+00 2.942344716e-01 3.2e-04 0.82 12 1.6e-04 1.6e-04 3.9e-04 8.42e-01 0.000000000e+00 1.601736349e-01 1.6e-04 0.88 13 6.6e-05 6.6e-05 2.3e-04 8.76e-01 0.000000000e+00 8.188877771e-02 6.6e-05 0.96 14 3.3e-05 3.3e-05 1.5e-04 7.84e-01 0.000000000e+00 4.487005438e-02 3.3e-05 1.01 15 1.9e-05 1.9e-05 1.2e-04 8.71e-01 0.000000000e+00 2.744132012e-02 1.9e-05 1.08 16 6.8e-06 6.8e-06 6.7e-05 9.23e-01 0.000000000e+00 1.021098843e-02 6.8e-06 1.15 17 2.3e-06 2.3e-06 3.8e-05 9.85e-01 0.000000000e+00 3.423811429e-03 2.3e-06 1.22 18 4.0e-07 3.9e-07 1.6e-05 9.96e-01 0.000000000e+00 6.055082514e-04 3.9e-07 1.28 19 9.8e-08 7.5e-08 6.8e-06 9.99e-01 0.000000000e+00 1.172050822e-04 7.5e-08 1.36 20 4.0e-08 1.8e-08 3.1e-06 1.00e+00 0.000000000e+00 2.379364530e-05 1.5e-08 1.42 21 1.9e-08 4.1e-09 1.5e-06 1.00e+00 0.000000000e+00 5.363435609e-06 3.4e-09 1.49 22 5.1e-09 1.0e-09 7.4e-07 1.00e+00 0.000000000e+00 1.379608167e-06 8.7e-10 1.62 23 1.6e-09 4.6e-10 4.2e-07 1.00e+00 0.000000000e+00 4.435858331e-07 2.8e-10 1.75 24 1.6e-09 4.6e-10 4.2e-07 1.00e+00 0.000000000e+00 4.435858331e-07 2.8e-10 2.30 Interior-point optimizer terminated. Time: 2.85.

Optimizer terminated. Time: 2.85

Interior-point solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : NEAR_OPTIMAL Primal. obj: 0.0000000000e+00 nrm: 1e+03 Viol. con: 1e-07 var: 0e+00 barvar: 0e+00 Dual. obj: 4.4358583313e-07 nrm: 1e+03 Viol. con: 0e+00 var: 3e-09 barvar: 2e-08 Total elapsed time = 5.53s Optimizer started. Conic interior-point optimizer started. Presolve started. Presolve terminated. Time: 0.01 0 1.5e+00 1.0e+00 1.0e+00 0.00e+00 0.000000000e+00 0.000000000e+00 1.0e+00 0.07 1 1.2e+00 7.7e-01 8.8e-01 2.08e+00 0.000000000e+00 9.686900451e-02 7.7e-01 0.12 2 6.7e-01 4.5e-01 5.6e-01 2.21e+00 0.000000000e+00 2.835332909e-01 4.5e-01 0.19 3 4.7e-01 3.1e-01 1.7e-01 -4.11e-01 0.000000000e+00 2.480070915e+00 3.1e-01 0.27 4 1.3e-01 8.5e-02 3.1e-02 2.46e-01 0.000000000e+00 6.892231397e+00 8.5e-02 0.32 5 3.3e-02 2.2e-02 7.8e-03 -3.67e-01 0.000000000e+00 7.656613217e+00 2.2e-02 0.39 6 2.0e-02 1.3e-02 5.0e-03 -2.36e-01 0.000000000e+00 6.435712946e+00 1.3e-02 0.46 7 1.3e-02 8.5e-03 3.3e-03 -1.86e-02 0.000000000e+00 6.380253179e+00 8.5e-03 0.49 8 5.7e-03 3.8e-03 9.2e-04 -7.78e-01 0.000000000e+00 1.687257722e+01 3.8e-03 0.56 9 2.1e-03 1.4e-03 2.3e-04 -7.44e-01 0.000000000e+00 3.569362337e+01 1.4e-03 0.58 10 4.2e-04 2.8e-04 2.3e-05 -9.00e-01 0.000000000e+00 1.539421755e+02 2.8e-04 0.65 11 6.8e-05 4.5e-05 1.5e-06 -9.86e-01 0.000000000e+00 9.301738914e+02 4.5e-05 0.72 12 1.5e-05 9.4e-06 1.4e-07 -9.97e-01 0.000000000e+00 4.399621146e+03 9.4e-06 0.78 13 8.6e-06 2.2e-06 1.6e-08 -9.95e-01 0.000000000e+00 1.843118218e+04 2.2e-06 0.85 14 5.4e-06 3.7e-07 1.3e-09 -9.41e-01 0.000000000e+00 8.417342274e+04 3.9e-07 0.93 15 3.3e-06 7.2e-08 1.4e-10 -7.30e-01 0.000000000e+00 2.633466394e+05 8.0e-08 1.00 16 5.3e-07 1.5e-08 1.1e-11 -7.94e-01 0.000000000e+00 1.224713582e+06 1.4e-08 1.08 17 2.4e-07 3.1e-09 1.1e-12 -9.82e-01 0.000000000e+00 6.082287381e+06 2.9e-09 1.15 18 7.6e-08 1.6e-09 1.2e-13 -9.85e-01 0.000000000e+00 2.682774392e+07 6.7e-10 1.28 19 7.6e-08 1.6e-09 1.2e-13 -9.91e-01 0.000000000e+00 2.682774392e+07 6.7e-10 1.83 Interior-point optimizer terminated. Time: 2.37.

Optimizer terminated. Time: 2.37

Interior-point solution summary Problem status : PRIMAL_INFEASIBLE Solution status : NEAR_PRIMAL_INFEASIBLE_CER Dual. obj: 1.3546392279e-01 nrm: 2e+02 Viol. con: 0e+00 var: 3e-11 barvar: 2e-09 Total elapsed time = 14.36s Total elapsed time = 16.33s Optimizer started. Conic interior-point optimizer started. Presolve started. Presolve terminated. Time: 0.01 0 1.0e+00 1.0e+00 1.0e+00 0.00e+00 0.000000000e+00 0.000000000e+00 1.0e+00 0.06 1 7.7e-01 7.7e-01 8.7e-01 2.08e+00 0.000000000e+00 9.817426029e-02 7.7e-01 0.13 2 4.5e-01 4.5e-01 5.6e-01 2.21e+00 0.000000000e+00 2.835099536e-01 4.5e-01 0.20 3 3.1e-01 3.1e-01 1.7e-01 -4.07e-01 0.000000000e+00 2.408784953e+00 3.1e-01 0.27 4 8.5e-02 8.5e-02 3.1e-02 2.38e-01 0.000000000e+00 6.782154952e+00 8.5e-02 0.33 5 2.2e-02 2.2e-02 7.8e-03 -3.75e-01 0.000000000e+00 7.650579901e+00 2.2e-02 0.40 6 1.3e-02 1.3e-02 5.2e-03 -2.16e-01 0.000000000e+00 6.180762331e+00 1.3e-02 0.46 7 7.2e-03 7.2e-03 3.6e-03 1.60e-01 0.000000000e+00 3.852387067e+00 7.2e-03 0.52 8 3.4e-03 3.4e-03 2.2e-03 4.83e-01 0.000000000e+00 2.183484698e+00 3.4e-03 0.59 9 1.2e-03 1.2e-03 1.2e-03 5.92e-01 0.000000000e+00 8.834949954e-01 1.2e-03 0.66 10 6.4e-04 6.4e-04 8.7e-04 8.24e-01 0.000000000e+00 5.179695844e-01 6.4e-04 0.72 11 3.2e-04 3.2e-04 5.8e-04 8.48e-01 0.000000000e+00 2.942348279e-01 3.2e-04 0.78 12 1.6e-04 1.6e-04 3.9e-04 8.42e-01 0.000000000e+00 1.601741221e-01 1.6e-04 0.85 13 6.6e-05 6.6e-05 2.3e-04 8.76e-01 0.000000000e+00 8.188838054e-02 6.6e-05 0.91 14 3.3e-05 3.3e-05 1.5e-04 7.84e-01 0.000000000e+00 4.486984484e-02 3.3e-05 0.98 15 1.9e-05 1.9e-05 1.2e-04 8.71e-01 0.000000000e+00 2.743815587e-02 1.9e-05 1.05 16 6.8e-06 6.8e-06 6.7e-05 9.23e-01 0.000000000e+00 1.021228635e-02 6.8e-06 1.11 17 2.3e-06 2.3e-06 3.8e-05 9.85e-01 0.000000000e+00 3.429048443e-03 2.3e-06 1.18 18 4.1e-07 3.9e-07 1.6e-05 9.96e-01 0.000000000e+00 6.074272240e-04 3.9e-07 1.25 19 9.9e-08 7.6e-08 6.9e-06 9.99e-01 0.000000000e+00 1.179217346e-04 7.6e-08 1.34 20 3.3e-08 1.6e-08 3.1e-06 1.00e+00 0.000000000e+00 2.392671668e-05 1.5e-08 1.40 21 7.2e-09 3.5e-09 1.5e-06 1.00e+00 0.000000000e+00 5.372004494e-06 3.4e-09 1.53 22 1.8e-09 9.1e-10 7.4e-07 1.00e+00 0.000000000e+00 1.374818621e-06 8.7e-10 1.66 23 1.4e-09 3.4e-10 4.2e-07 1.00e+00 0.000000000e+00 4.355338963e-07 2.8e-10 1.78 24 1.4e-09 3.4e-10 4.2e-07 1.00e+00 0.000000000e+00 4.355338963e-07 2.8e-10 2.34 Interior-point optimizer terminated. Time: 2.89.

Optimizer terminated. Time: 2.89

Interior-point solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : NEAR_OPTIMAL Primal. obj: 0.0000000000e+00 nrm: 1e+03 Viol. con: 7e-08 var: 0e+00 barvar: 0e+00 Dual. obj: 4.3553389633e-07 nrm: 1e+03 Viol. con: 0e+00 var: 3e-09 barvar: 1e-08 Optimizer started. Conic interior-point optimizer started. Presolve started. Presolve terminated. Time: 0.01 0 1.0e+00 1.0e+00 1.0e+00 0.00e+00 0.000000000e+00 0.000000000e+00 1.0e+00 0.06 1 7.7e-01 7.7e-01 8.7e-01 2.08e+00 0.000000000e+00 9.817426029e-02 7.7e-01 0.13 2 4.5e-01 4.5e-01 5.6e-01 2.21e+00 0.000000000e+00 2.835099536e-01 4.5e-01 0.19 3 3.1e-01 3.1e-01 1.7e-01 -4.07e-01 0.000000000e+00 2.408784953e+00 3.1e-01 0.26 4 8.5e-02 8.5e-02 3.1e-02 2.38e-01 0.000000000e+00 6.782154949e+00 8.5e-02 0.33 5 2.2e-02 2.2e-02 7.8e-03 -3.75e-01 0.000000000e+00 7.650579911e+00 2.2e-02 0.39 6 1.3e-02 1.3e-02 5.2e-03 -2.16e-01 0.000000000e+00 6.180762352e+00 1.3e-02 0.45 7 7.2e-03 7.2e-03 3.6e-03 1.60e-01 0.000000000e+00 3.852387177e+00 7.2e-03 0.52 8 3.4e-03 3.4e-03 2.2e-03 4.83e-01 0.000000000e+00 2.183484764e+00 3.4e-03 0.58 9 1.2e-03 1.2e-03 1.2e-03 5.92e-01 0.000000000e+00 8.834949264e-01 1.2e-03 0.65 10 6.4e-04 6.4e-04 8.7e-04 8.24e-01 0.000000000e+00 5.179695823e-01 6.4e-04 0.72 11 3.2e-04 3.2e-04 5.8e-04 8.48e-01 0.000000000e+00 2.942344716e-01 3.2e-04 0.79 12 1.6e-04 1.6e-04 3.9e-04 8.42e-01 0.000000000e+00 1.601736349e-01 1.6e-04 0.85 13 6.6e-05 6.6e-05 2.3e-04 8.76e-01 0.000000000e+00 8.188877771e-02 6.6e-05 0.91 14 3.3e-05 3.3e-05 1.5e-04 7.84e-01 0.000000000e+00 4.487005438e-02 3.3e-05 0.98 15 1.9e-05 1.9e-05 1.2e-04 8.71e-01 0.000000000e+00 2.744132012e-02 1.9e-05 1.04 16 6.8e-06 6.8e-06 6.7e-05 9.23e-01 0.000000000e+00 1.021098843e-02 6.8e-06 1.11 17 2.3e-06 2.3e-06 3.8e-05 9.85e-01 0.000000000e+00 3.423811429e-03 2.3e-06 1.18 18 4.0e-07 3.9e-07 1.6e-05 9.96e-01 0.000000000e+00 6.055082514e-04 3.9e-07 1.23 19 9.8e-08 7.5e-08 6.8e-06 9.99e-01 0.000000000e+00 1.172050822e-04 7.5e-08 1.32 20 4.0e-08 1.8e-08 3.1e-06 1.00e+00 0.000000000e+00 2.379364530e-05 1.5e-08 1.39 21 1.9e-08 4.1e-09 1.5e-06 1.00e+00 0.000000000e+00 5.363435609e-06 3.4e-09 1.45 22 5.1e-09 1.0e-09 7.4e-07 1.00e+00 0.000000000e+00 1.379608167e-06 8.7e-10 1.58 23 1.6e-09 4.6e-10 4.2e-07 1.00e+00 0.000000000e+00 4.435858331e-07 2.8e-10 1.71 24 1.6e-09 4.6e-10 4.2e-07 1.00e+00 0.000000000e+00 4.435858331e-07 2.8e-10 2.26 Interior-point optimizer terminated. Time: 2.81.

Optimizer terminated. Time: 2.81

Interior-point solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : NEAR_OPTIMAL Primal. obj: 0.0000000000e+00 nrm: 1e+03 Viol. con: 1e-07 var: 0e+00 barvar: 0e+00 Dual. obj: 4.4358583313e-07 nrm: 1e+03 Viol. con: 0e+00 var: 3e-09 barvar: 2e-08 Total elapsed time = 25.20s

Nodes    |    Current Node    |     Objective Bounds      |     Work

Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time

  • 0 0 0 0.0000000 0.00000 - - 29s

Cutting planes: Lazy constraints: 512

Explored 0 nodes (41442 simplex iterations) in 29.34 seconds Thread count was 4 (of 4 available processors)

Solution count 1: 0 Pool objective bound 0

Optimal solution found (tolerance 1.00e-04) Best objective 0.000000000000e+00, best bound 0.000000000000e+00, gap -

MIP-solver-driven algorithm summary:

  • Status = Optimal
  • Best feasible = +Inf
  • Best bound = +0.000000e+00
  • Relative opt. gap = NaN
  • Total time (s) = 3.25e+01

So the status is optimal, but the optimal solution is a vector of NaNs.

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chriscoey commented 7 years ago

also can you use log_level=3 so we can see more output at the end

probably the weird statuses that MOSEK seems to be returning is related to this error

mlubin commented 7 years ago

Looks like a symptom of solver statuses being broken in MPB. Mosek never reports :Optimal so we don't have a solution.

chriscoey commented 7 years ago

you could also try turning off the conic solves to do primal separation cuts only. don't pass in a conic solver, and set prim_cuts_only=true (maybe also need to set solve_relax=false and solve_subp=false)

joehuchette commented 7 years ago

Log level 3:

Problem dimensions:
       variables |      2904
     constraints |      1056
   nonzeros in A |      6480

Cones summary:
Cone             | Count     | Min dim.  | Max dim.
   Pos. semidef. |       432 |       3^2 |       3^2

Variable types:
      continuous |      2892
          binary |        12

Transforming data...               0.00s

Creating conic subproblem...       0.02s

Building MIP model...              0.03s

Solving conic relaxation...      Problem
  Name                   :
  Objective sense        : min
  Type                   : CONIC (conic optimization problem)
  Constraints            : 3648
  Cones                  : 0
  Scalar variables       : 2904
  Matrix variables       : 432
  Integer variables      : 0

Optimizer started.
Conic interior-point optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 932
Eliminator terminated.
Eliminator started.
Freed constraints in eliminator : 7
Eliminator terminated.
Eliminator - tries                  : 2                 time                   : 0.00
Lin. dep.  - tries                  : 1                 time                   : 0.00
Lin. dep.  - number                 : 0
Presolve terminated. Time: 0.01
Optimizer  - threads                : 4
Optimizer  - solved problem         : the primal
Optimizer  - Constraints            : 2694
Optimizer  - Cones                  : 1
Optimizer  - Scalar variables       : 1963              conic                  : 1939
Optimizer  - Semi-definite variables: 432               scalarized             : 2592
Factor     - setup time             : 0.01              dense det. time        : 0.00
Factor     - ML order time          : 0.00              GP order time          : 0.00
Factor     - nonzeros before factor : 2.11e+04          after factor           : 2.62e+04
Factor     - dense dim.             : 2                 flops                  : 4.10e+05
ITE PFEAS    DFEAS    GFEAS    PRSTATUS   POBJ              DOBJ              MU       TIME
0   1.0e+00  1.0e+00  1.0e+00  0.00e+00   0.000000000e+00   0.000000000e+00   1.0e+00  0.04
1   7.0e-01  7.0e-01  8.9e-01  1.36e+00   0.000000000e+00   -1.511306070e-02  7.0e-01  0.08
2   3.6e-01  3.6e-01  4.9e-01  1.68e+00   0.000000000e+00   1.966856386e-01   3.6e-01  0.12
3   1.7e-01  1.7e-01  8.2e-02  -6.34e-01  0.000000000e+00   3.156971504e+00   1.7e-01  0.15
4   3.6e-02  3.6e-02  1.2e-02  -1.21e-01  0.000000000e+00   7.833804095e+00   3.6e-02  0.20
5   1.3e-02  1.3e-02  5.7e-03  1.21e-01   0.000000000e+00   4.843041541e+00   1.3e-02  0.24
6   8.2e-03  8.2e-03  4.2e-03  3.27e-01   0.000000000e+00   3.527386169e+00   8.2e-03  0.27
7   3.1e-03  3.1e-03  2.0e-03  3.98e-01   0.000000000e+00   2.177742421e+00   3.1e-03  0.31
8   1.2e-03  1.2e-03  1.2e-03  7.47e-01   0.000000000e+00   8.904188287e-01   1.2e-03  0.34
9   6.4e-04  6.4e-04  7.1e-04  6.31e-01   0.000000000e+00   7.862199571e-01   6.4e-04  0.38
10  3.2e-04  3.2e-04  4.8e-04  7.22e-01   0.000000000e+00   4.316633357e-01   3.2e-04  0.40
11  1.1e-04  1.1e-04  2.7e-04  8.36e-01   0.000000000e+00   1.807787944e-01   1.1e-04  0.43
12  4.6e-05  4.6e-05  1.6e-04  8.52e-01   0.000000000e+00   8.518432599e-02   4.6e-05  0.47
13  1.8e-05  1.8e-05  8.9e-05  8.80e-01   0.000000000e+00   3.805150250e-02   1.8e-05  0.50
14  1.3e-05  1.3e-05  7.5e-05  8.73e-01   0.000000000e+00   2.788684368e-02   1.3e-05  0.53
15  3.0e-06  3.0e-06  3.5e-05  9.08e-01   0.000000000e+00   7.256958134e-03   3.0e-06  0.57
16  9.1e-07  9.0e-07  1.9e-05  9.96e-01   0.000000000e+00   2.204207562e-03   9.0e-07  0.61
17  3.3e-07  1.6e-07  7.9e-06  1.00e+00   0.000000000e+00   3.846991109e-04   1.6e-07  0.65
18  1.1e-07  3.3e-08  3.6e-06  1.00e+00   0.000000000e+00   8.090592542e-05   3.3e-08  0.69
19  4.9e-08  6.8e-09  1.6e-06  1.00e+00   0.000000000e+00   1.635865759e-05   6.6e-09  0.73
20  4.6e-08  6.3e-09  1.5e-06  1.00e+00   0.000000000e+00   1.476218063e-05   5.9e-09  0.85
21  4.6e-08  6.3e-09  1.5e-06  1.00e+00   0.000000000e+00   1.476218063e-05   5.9e-09  1.17
Interior-point optimizer terminated. Time: 1.47.

Optimizer terminated. Time: 1.47

Interior-point solution summary
  Problem status  : PRIMAL_AND_DUAL_FEASIBLE
  Solution status : NEAR_OPTIMAL
  Primal.  obj: 0.0000000000e+00    nrm: 1e+03    Viol.  con: 2e-03    var: 0e+00    barvar: 0e+00
  Dual.    obj: 1.4762180626e-05    nrm: 9e+02    Viol.  con: 2e-07    var: 1e-07    barvar: 3e-07
  1.49s
WARNING: Conic solver failure on initial relaxation: returned status Stall

Starting MIP-solver-driven algorithm
Optimize a model with 4944 rows, 2904 columns and 15552 nonzeros
Variable types: 2892 continuous, 12 integer (12 binary)
Coefficient statistics:
  Matrix range     [8e-08, 1e+01]
  Objective range  [0e+00, 0e+00]
  Bounds range     [0e+00, 0e+00]
  RHS range        [8e-02, 1e+00]
Presolve removed 1466 rows and 152 columns
Presolve time: 0.01s
Presolved: 3478 rows, 2752 columns, 13417 nonzeros
Variable types: 2740 continuous, 12 integer (12 binary)

Root relaxation: objective 0.000000e+00, 2172 iterations, 0.14 seconds
Problem
  Name                   :
  Objective sense        : min
  Type                   : CONIC (conic optimization problem)
  Constraints            : 3636
  Cones                  : 0
  Scalar variables       : 2892
  Matrix variables       : 432
  Integer variables      : 0

Optimizer started.
Conic interior-point optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 932
Eliminator terminated.
Eliminator started.
Freed constraints in eliminator : 7
Eliminator terminated.
Eliminator - tries                  : 2                 time                   : 0.00
Lin. dep.  - tries                  : 1                 time                   : 0.00
Lin. dep.  - number                 : 0
Presolve terminated. Time: 0.01
Optimizer  - threads                : 4
Optimizer  - solved problem         : the primal
Optimizer  - Constraints            : 2694
Optimizer  - Cones                  : 1
Optimizer  - Scalar variables       : 1951              conic                  : 1939
Optimizer  - Semi-definite variables: 432               scalarized             : 2592
Factor     - setup time             : 0.01              dense det. time        : 0.00
Factor     - ML order time          : 0.00              GP order time          : 0.00
Factor     - nonzeros before factor : 2.11e+04          after factor           : 2.62e+04
Factor     - dense dim.             : 2                 flops                  : 4.10e+05
ITE PFEAS    DFEAS    GFEAS    PRSTATUS   POBJ              DOBJ              MU       TIME
0   1.0e+00  1.0e+00  1.0e+00  0.00e+00   0.000000000e+00   0.000000000e+00   1.0e+00  0.04
1   7.0e-01  7.0e-01  8.8e-01  1.61e+00   0.000000000e+00   1.955183277e-02   7.0e-01  0.07
2   3.8e-01  3.8e-01  4.8e-01  1.86e+00   0.000000000e+00   2.620269925e-01   3.8e-01  0.11
3   1.5e-01  1.5e-01  5.9e-02  -6.68e-01  0.000000000e+00   5.417216360e+00   1.5e-01  0.14
4   3.5e-02  3.5e-02  1.6e-02  1.64e-01   0.000000000e+00   4.258915625e+00   3.5e-02  0.17
5   1.3e-02  1.3e-02  6.2e-03  -2.72e-01  0.000000000e+00   4.358975287e+00   1.3e-02  0.21
6   8.0e-03  8.0e-03  4.3e-03  1.53e-01   0.000000000e+00   3.215923339e+00   8.0e-03  0.25
7   3.2e-03  3.2e-03  2.3e-03  4.02e-01   0.000000000e+00   1.859510765e+00   3.2e-03  0.28
8   1.3e-03  1.3e-03  1.4e-03  6.87e-01   0.000000000e+00   7.972062099e-01   1.3e-03  0.31
9   7.3e-04  7.3e-04  8.4e-04  7.34e-01   0.000000000e+00   7.176892921e-01   7.3e-04  0.35
10  3.2e-04  3.2e-04  5.3e-04  7.54e-01   0.000000000e+00   3.412014633e-01   3.2e-04  0.38
11  1.6e-04  1.6e-04  3.6e-04  9.00e-01   0.000000000e+00   1.853993690e-01   1.6e-04  0.41
12  8.5e-05  8.5e-05  2.5e-04  9.03e-01   0.000000000e+00   1.077982672e-01   8.5e-05  0.45
13  2.6e-05  2.6e-05  1.3e-04  9.18e-01   0.000000000e+00   3.759586461e-02   2.6e-05  0.48
14  1.1e-05  1.1e-05  8.1e-05  8.73e-01   0.000000000e+00   1.897487980e-02   1.1e-05  0.52
15  4.7e-06  4.7e-06  5.2e-05  9.56e-01   0.000000000e+00   7.942888055e-03   4.7e-06  0.55
16  1.2e-06  1.2e-06  2.6e-05  9.94e-01   0.000000000e+00   2.062327235e-03   1.2e-06  0.58
17  2.5e-07  2.3e-07  1.1e-05  1.00e+00   0.000000000e+00   3.881182895e-04   2.3e-07  0.62
18  1.8e-07  5.2e-08  5.4e-06  1.00e+00   0.000000000e+00   8.863224881e-05   5.2e-08  0.65
19  5.7e-08  1.0e-08  2.4e-06  1.00e+00   0.000000000e+00   1.744012235e-05   1.0e-08  0.68
20  3.9e-08  6.1e-09  1.9e-06  1.00e+00   0.000000000e+00   1.035306726e-05   6.0e-09  0.78
21  3.9e-08  6.1e-09  1.9e-06  1.00e+00   0.000000000e+00   1.035306726e-05   6.0e-09  1.06
Interior-point optimizer terminated. Time: 1.38.

Optimizer terminated. Time: 1.38

Interior-point solution summary
  Problem status  : PRIMAL_AND_DUAL_FEASIBLE
  Solution status : NEAR_OPTIMAL
  Primal.  obj: 0.0000000000e+00    nrm: 1e+03    Viol.  con: 2e-03    var: 0e+00    barvar: 0e+00
  Dual.    obj: 1.0353067259e-05    nrm: 1e+03    Viol.  con: 0e+00    var: 9e-08    barvar: 3e-07
Total elapsed time = 5.75s
Optimizer started.
Conic interior-point optimizer started.
Presolve started.
Presolve terminated. Time: 0.01
0   1.0e+00  1.0e+00  1.0e+00  0.00e+00   0.000000000e+00   0.000000000e+00   1.0e+00  0.03
1   7.0e-01  7.0e-01  8.8e-01  1.61e+00   0.000000000e+00   1.955183264e-02   7.0e-01  0.07
2   3.8e-01  3.8e-01  4.8e-01  1.86e+00   0.000000000e+00   2.620269998e-01   3.8e-01  0.10
3   1.5e-01  1.5e-01  5.9e-02  -6.68e-01  0.000000000e+00   5.417216287e+00   1.5e-01  0.13
4   3.5e-02  3.5e-02  1.6e-02  1.64e-01   0.000000000e+00   4.258915728e+00   3.5e-02  0.17
5   1.3e-02  1.3e-02  6.2e-03  -2.72e-01  0.000000000e+00   4.358975376e+00   1.3e-02  0.21
6   8.0e-03  8.0e-03  4.3e-03  1.53e-01   0.000000000e+00   3.215923434e+00   8.0e-03  0.24
7   3.2e-03  3.2e-03  2.3e-03  4.02e-01   0.000000000e+00   1.859510901e+00   3.2e-03  0.28
8   1.3e-03  1.3e-03  1.4e-03  6.87e-01   0.000000000e+00   7.972064444e-01   1.3e-03  0.31
9   7.3e-04  7.3e-04  8.4e-04  7.34e-01   0.000000000e+00   7.176895391e-01   7.3e-04  0.35
10  3.2e-04  3.2e-04  5.3e-04  7.54e-01   0.000000000e+00   3.412020984e-01   3.2e-04  0.38
11  1.6e-04  1.6e-04  3.6e-04  9.00e-01   0.000000000e+00   1.854020796e-01   1.6e-04  0.41
12  8.5e-05  8.5e-05  2.5e-04  9.03e-01   0.000000000e+00   1.078009771e-01   8.5e-05  0.45
13  2.6e-05  2.6e-05  1.3e-04  9.18e-01   0.000000000e+00   3.759866401e-02   2.6e-05  0.48
14  1.1e-05  1.1e-05  8.1e-05  8.73e-01   0.000000000e+00   1.898075790e-02   1.1e-05  0.51
15  4.7e-06  4.7e-06  5.2e-05  9.56e-01   0.000000000e+00   7.942210857e-03   4.7e-06  0.55
16  1.2e-06  1.2e-06  2.6e-05  9.93e-01   0.000000000e+00   2.058938086e-03   1.2e-06  0.58
17  2.4e-07  2.3e-07  1.1e-05  1.00e+00   0.000000000e+00   3.899709671e-04   2.3e-07  0.62
18  1.1e-07  4.6e-08  5.1e-06  9.99e-01   0.000000000e+00   7.936082789e-05   4.6e-08  0.66
19  4.4e-08  9.0e-09  2.2e-06  9.89e-01   0.000000000e+00   1.602770579e-05   8.9e-09  0.70
20  4.4e-08  9.0e-09  2.2e-06  9.41e-01   0.000000000e+00   1.602770579e-05   8.9e-09  1.01
Interior-point optimizer terminated. Time: 1.29.

Optimizer terminated. Time: 1.29

Interior-point solution summary
  Problem status  : PRIMAL_AND_DUAL_FEASIBLE
  Solution status : NEAR_OPTIMAL
  Primal.  obj: 0.0000000000e+00    nrm: 1e+03    Viol.  con: 1e-03    var: 0e+00    barvar: 0e+00
  Dual.    obj: 1.6027705791e-05    nrm: 1e+03    Viol.  con: 0e+00    var: 1e-07    barvar: 4e-07

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0       0.0000000    0.00000      -     -    9s

Cutting planes:
  Lazy constraints: 299

Explored 0 nodes (23838 simplex iterations) in 9.35 seconds
Thread count was 4 (of 4 available processors)

Solution count 1: 0
Pool objective bound 0

Optimal solution found (tolerance 1.00e-04)
Best objective 0.000000000000e+00, best bound 0.000000000000e+00, gap -

MIP-solver-driven algorithm summary:
 - Status               =        Optimal
 - Best feasible        =           +Inf
 - Best bound           =  +0.000000e+00
 - Relative opt. gap    =            NaN
 - Total time (s)       =       1.09e+01

Timers (s):
 - Setup                =   5.28e-02
 -- Transform data      =   3.32e-03
 -- Create conic data   =   1.72e-02
 -- Create MIP data     =   3.23e-02
 - Algorithm            =   1.09e+01
 -- Solve relaxation    =   1.49e+00
 -- Get relaxation cuts =   0.00e+00
 -- MIP solver driving  =   9.35e+00
 -- Solve subproblems   =   2.67e+00
 -- Get subproblem cuts =   3.25e-01
 -- Get primal cuts     =   9.22e-02

Counters:
 - Lazy callbacks       =    12
 -- Integer repeats     =    10
 -- Conic subproblems   =     2
 --- Infeasible         =     0
 --- Optimal            =     0
 --- Suboptimal         =     0
 --- UserLimit          =     0
 --- ConicFailure       =     0
 --- Other status       =     2
 -- Feasible solutions  =     0
 --- From subproblems   =     0
 --- In lazy callback   =     0
 - Heuristic callbacks  =     0
 -- Solutions passed    =     0

Solution returned by MIP solver

Outer-approximation cuts added:
Cone             | Relax.    | Violated  | Nonviol.
   Pos. semidef. |         0 |       314 |         0

0 numerically unstable cone duals encountered

This is on Pajarito v0.3.2.

mlubin commented 7 years ago

This is on Pajarito v0.3.2.

That's ancient. Use 0.4.2 or master.

joehuchette commented 7 years ago

Sorry, it is 0.4.2.

joehuchette commented 7 years ago

On Pajarito master:

WARNING: Pajarito failed to converge to the desired relative gap; try turning off the MIP solver's presolve functionality

MIP-solver-driven algorithm summary:
 - Status               =       FailedOA
 - Best feasible        =           +Inf
 - Best bound           =  +0.000000e+00
 - Relative opt. gap    =            NaN
 - Total time (s)       =       1.61e+01

Timers (s):
 - Setup                =   3.69e+00
 -- Transform data      =   6.41e-01
 -- Create conic data   =   1.69e+00
 -- Create MIP data     =   1.35e+00
 - Algorithm            =   1.25e+01
 -- Solve relaxation    =   1.53e+00
 -- Get relaxation cuts =   0.00e+00
 -- MIP solver driving  =   1.08e+01
 -- Solve subproblems   =   3.54e+00
 -- Get subproblem cuts =   7.97e-01
 -- Get separation cuts =   8.92e-02

Counters:
 - Lazy callbacks       =    14
 -- Integer repeats     =    11
 -- Conic subproblems   =     3
 --- Infeasible         =     0
 --- Optimal            =     0
 --- Suboptimal         =     0
 --- UserLimit          =     0
 --- ConicFailure       =     0
 --- Other status       =     3
 -- Feasible solutions  =     0
 --- From subproblems   =     0
 --- In lazy callback   =     0
 - Heuristic callbacks  =     0
 -- Solutions passed    =     0

Solution returned by MIP solver

Rounds of full separation/subproblem cuts, and count of cuts added:
Cone             | Subp.  | Sep.   | Total  | Relax. | Viol.
   Pos. semidef. |   4032 |      0 |    715 |      0 |    715

WARNING: Not solved to optimality, status: FailedOA
chriscoey commented 7 years ago

OK, looks like master is better at handling the issue at least. I'd stick with master for your tests, unless something else spectacularly breaks (I won't have time to fix anything, generals in a week).

chriscoey commented 7 years ago

Did you try iterative rather than MSD?

chriscoey commented 7 years ago

@mlubin it's reasonably likely that release is more buggy than master anyway - maybe Tristan should be on master

chriscoey commented 7 years ago

@joehuchette it's a long shot, but you could try SCS (you can also try setting warm_start=true in SCS options). play with SCS tolerances - if it fails at eps = 1e-6, try 1e-5, 1e-4, 1e-3. check the PSD conic infeasibility of Pajarito solutions (if you get any) by looking at the bottom of the output with log_level=3

chriscoey commented 7 years ago

you can also try changing mosek tolerances too - they probably don't need to be as tight as they are at default. see http://docs.mosek.com/8.0/capi/solving-conic.html

chriscoey commented 7 years ago

hopefully this issue should be fixed after MPB and JuMP rework statuses https://github.com/JuliaOpt/MathProgBase.jl/issues/164