Moré - Garbow - Hillstrom test set

[tmigot]

Moré - Garbow - Hillstrom test set

Moré, J. J., Garbow, B. S., & Hillstrom, K. E. (1981). Testing Unconstrained Optimization Software. ACM Transactions on Mathematical Software, 7(1), 17–41. https://dl.acm.org/doi/10.1145/355934.355936

Suggested in https://github.com/JuliaSmoothOptimizers/OptimizationProblems.jl/issues/7

Name in the report	Type of problems	Implemented in JSO?	name of the file in JSO

• [x] Rosenbrock function (1) (OP) genrose.jl (function rosenbrock)
• [X] Freudenstein and Roth function (2) (NLS) freuroth.jl
• [x] Powell badly scaled function (3) (OP)
• [X] Brown badly scaled function (4) (OP) brownbs.jl
• [X] Beale function (5) (OP) beale.jl
• [x] Jennrich and Sampson function (6) (NLS)
• [x] Helical valley function (7) (OP)
• [x] Bard function (8) (NLS)
• [x] Gaussian function (9) (OP)
• [X] Meyer function (10) (NLS) meyer3.jl
• [x] Gulf research and development function (11) (OP)
• [x] Box three-dimensional function (12) (NLS)
• [X] Powell singular function (13) (OP) powellsg.jl
• [X] Wood function (14) (OP) woods.jl
• [x] Kowalik and Osborne function (15) (NLS)
• [X] Brown and Dennis function (16) (NLS) brownden.jl
• [x] Osborne i function (17) (NLS)
• [x] Biggs EXP6 function (18) (OP)
• [x] Osborne 2 function (19) (NLS)
• [x] Watson function (20) (OP)
• [X] Extended Rosenbrock function (21) (OP) srosenbr.jl
• [x] Extended Powell singular function (22) (OP)
• [x] Penalty function I (23) (OP)
• [X] Penalty function II (24) (OP) penalty2.jl
• [X] Variably dimensioned function (25) (OP) vardim.jl
• [x] Trigonometric function (26) (OP)
• [x] Brown almost-linear function (27) (OP)
• [X] Discrete boundary value function (28) (OP) morebv.jl
• [x] Discrete integral equation function (29) (OP)
• [x] Broyden tridiagonal function (30) (OP)
• [X] Broyden banded function (31) (OP) brybnd. jl (sbrybnd.jl is an unscaled version)
• [X] Linear function - full rank (32) (NLS) arglina.jl
• [X] Linear function - rank 1 (33) (NLS) arglinb.jl
• [X] Linear function - rank 1 with zero columns and rows (34) (NLS) arglinc.jl
• [ ] Chebyquad function (35) (OP)

[tmigot]

The difficulty for the last problem is with the JuMP Model.

The issue is with the computation of the Chebyshev polynomials that are defined recursively. I tried things like

m = n = 100
function Chbi(y::T, m) where {T} # Chebyshev polynomial of the first kind
    res = zeros(T, m)
    m = Int(m)
    res[1] = 1 # T0
    if i == 1
      return res
    end
    res[2] = y
    if m == 2
      return res
    end
    for j=2:m
      res[2 + j] = 2 * y * res[j + 1] - res[j]
    end
    return res[end]
  end
  register(nlp, :Chbi, 2, Chbi, autodiff = true)

doesn't work because it supports only real arguments.

@amontoison any idea?

[amontoison]

The issue is if ... else ... end. We can't easily handle them in automatic differentiation. The issue that you opened in ADNLPModels.jl is probably related.

[amontoison]

Sorry Tangi, I misunderstood the issue. Can you definite the function in the the function that definites the JuMP model such that you can remove the argument m?

[tmigot]

Well, it's true we could try to simplify the sum in NLobjective but I had similar issues for other models as well and was wondering if there was a simpler solution.

[dpo]

I think there’s a problem here with at least certain models of this collection. They are created as ADNLPModels while they should be ADNLSModels. For example, here is how biggs6 (problem 18) is created:

https://github.com/JuliaSmoothOptimizers/OptimizationProblems.jl/blob/main/src/ADNLPProblems/biggs6.jl#L15

If you try to solve this problem, you find that it’s unbounded. Of course, that doesn’t make any sense, because it should be a nonlinear least-squares objective.

Perhaps other NLS problems are affected as well.