bodono
commented
3 years ago When I run your code (with verbose=True) I get:
----------------------------------------------------------------------------
SCS v2.1.2 - Splitting Conic Solver
(c) Brendan O'Donoghue, Stanford University, 2012
----------------------------------------------------------------------------
Lin-sys: sparse-direct, nnz in A = 40
eps = 1.00e-04, alpha = 1.50, max_iters = 5000, normalize = 1, scale = 1.00
acceleration_lookback = 10, rho_x = 1.00e-03
Variables n = 12, constraints m = 33
Cones: linear vars: 2
sd vars: 31, sd blks: 5
Setup time: 2.67e-04s
----------------------------------------------------------------------------
Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)
----------------------------------------------------------------------------
0| 3.41e+19 2.50e+19 9.87e-01 5.89e+20 8.98e+22 4.83e+22 7.68e-04
100| 3.66e-03 5.93e-03 4.13e-02 7.94e+01 8.63e+01 9.05e-14 3.40e-03
200| 3.71e-04 2.91e-04 8.44e-04 7.68e+01 7.67e+01 3.39e-13 5.14e-03
300| 8.22e-04 9.25e-04 4.90e-03 7.70e+01 7.78e+01 4.75e-14 6.67e-03
400| 5.32e-04 7.56e-04 1.64e-03 7.69e+01 7.67e+01 2.68e-14 8.17e-03
500| 2.56e-04 6.32e-04 2.32e-03 7.62e+01 7.66e+01 2.39e-13 9.69e-03
600| 2.69e+18 5.12e+17 9.36e-01 -5.08e+19 -1.69e+18 6.37e+20 1.12e-02
700| 4.53e-05 3.57e-05 7.74e-04 7.94e+01 7.96e+01 1.03e-13 1.28e-02
760| 9.86e-06 2.97e-06 1.79e-07 7.91e+01 7.91e+01 1.30e-13 1.37e-02
----------------------------------------------------------------------------
Status: Solved
Timing: Solve time: 1.37e-02s
Lin-sys: nnz in L factor: 87, avg solve time: 3.41e-07s
Cones: avg projection time: 1.31e-05s
Acceleration: avg step time: 3.52e-06s
----------------------------------------------------------------------------
Error metrics:
dist(s, K) = 2.1514e-09, dist(y, K*) = 2.2195e-09, s'y/|s||y| = -1.2370e-11
primal res: |Ax + s - b|_2 / (1 + |b|_2) = 9.8637e-06
dual res: |A'y + c|_2 / (1 + |c|_2) = 2.9723e-06
rel gap: |c'x + b'y| / (1 + |c'x| + |b'y|) = 1.7878e-07
----------------------------------------------------------------------------
c'x = 79.1368, -b'y = 79.1369
============================================================================
Optimal Value (SCS): 0.025195336215986686 solver time: 13.736438I don't have a MOSEK license so I can't run the rest, but it looks to me like it's solving the problem fine. I can run it with CVXOPT, which gets:
pcost dcost gap pres dres k/t
0: 9.4227e+02 7.3368e+02 1e+04 2e+00 3e-01 1e+00
1: 1.0471e+02 4.5939e+01 3e+04 1e+00 2e-01 1e+02
2: 8.2810e+02 1.6318e+03 5e+04 1e+00 2e-01 9e+02
3: 1.1637e+03 1.7584e+03 2e+04 5e-01 8e-02 7e+02
4: -3.4335e+02 1.3772e+02 1e+04 3e-01 5e-02 5e+02
5: -3.4805e+01 4.9283e+01 2e+03 6e-02 1e-02 9e+01
6: 6.2995e+01 8.0625e+01 3e+02 1e-02 2e-03 2e+01
7: 7.6330e+01 7.8702e+01 4e+01 1e-03 2e-04 3e+00
8: 7.8529e+01 7.9122e+01 1e+01 4e-04 6e-05 6e-01
9: 7.9010e+01 7.9098e+01 2e+00 5e-05 9e-06 9e-02
10: 7.9124e+01 7.9136e+01 2e-01 7e-06 1e-06 1e-02
11: 7.9132e+01 7.9137e+01 9e-02 3e-06 4e-07 6e-03
12: 7.9135e+01 7.9137e+01 2e-02 6e-07 9e-08 2e-03
13: 7.9131e+01 7.9132e+01 1e-02 2e-07 4e-08 1e-03
14: 7.9129e+01 7.9130e+01 8e-03 1e-07 2e-08 6e-04
15: 7.9128e+01 7.9129e+01 2e-02 2e-07 3e-08 1e-03
16: 7.9128e+01 7.9128e+01 1e-02 1e-07 2e-08 6e-04
17: 7.9125e+01 7.9125e+01 4e-03 3e-08 4e-09 3e-04
18: 7.9124e+01 7.9124e+01 5e-03 2e-08 3e-09 3e-04
19: 7.9123e+01 7.9123e+01 2e-03 5e-09 7e-10 1e-04
20: 7.9122e+01 7.9123e+01 2e-03 1e-07 1e-07 1e-04
21: 7.9122e+01 7.9123e+01 5e-05 1e-07 3e-08 3e-06
Terminated (singular KKT matrix).Unfortunately CVXOPT fails as it runs into numerical difficulties, but the objective value it is converging to is roughly 79.122, and SCS is getting 79.1368, so they are very close and looks like SCS is solving it correctly. What's the issue?
astghikhakobyan
Hello,
I am using SCS for solving an SDP problem in cvxpy. However, the result I get is incorrect when I compare it to other solvers such as MOSEK, SEDUMI, and SDPT3. All three solvers return somewhat similar results, while the SCS one is completely different. Similarly, when I solve the dual version of my problem, in the case of MOSEK the optimal values are very close, while in the case of SCS completely different. Please see below my python code.
import cvxpy as cp import numpy as np
ny = 2 p = 3 theta = 0.0001 alpha = 0.95 r = 0.2
Z = cp.Variable((ny,ny), PSD=True) z = cp.Variable((1,1)) tau = cp.Variable((1,1)) lambda1 = cp.Variable() eps = cp.Variable((1,1)) gamma = cp.Variable((ny,1)) Gamma = cp.Variable((ny,ny), symmetric=True) mu_hat = cp.Parameter(ny) Sigma_hat = cp.Parameter(ny+1) y = cp.Parameter(ny) mu_hat1 = cp.Parameter(1) Sigma_hat1 = cp.Parameter(ny+1) y1 = cp.Parameter(1)
Sigma = cp.Expression() Sigma = cp.bmat([[Sigma_hat[0], Sigma_hat[1]],[Sigma_hat[1], Sigma_hat[2]]]) Sigma1 = cp.Expression() Sigma1 = cp.bmat([[Sigma_hat1[0], Sigma_hat1[1]],[Sigma_hat1[1], Sigma_hat1[2]]])
constraints = [ cp.bmat([[lambda1 np.eye(ny) - Gamma, gamma + cp.vstack(lambda1 mu_hat)], [(gamma + cp.vstack(lambda1 mu_hat)).T, eps] ]) >> 0, cp.bmat([[lambda1 np.eye(ny) - Gamma, lambda1 Sigma], [(lambda1 Sigma).T, Z] ]) >> 0, cp.bmat([[np.eye(ny) + Gamma, gamma - cp.vstack(y)], [(gamma - cp.vstack(y)).T, tau + z] ]) >> 0, cp.bmat([[Gamma, gamma], [gamma.T, tau] ]) >> 0, eps >= 0, lambda1 >= 0 ] obj = cp.Minimize(- y1 + r r + z + 1/(1 - alpha) (tau + eps + cp.trace(Z) + lambda1 (theta theta - mu_hat1 - cp.trace(Sigma1))) ) prob = cp.Problem(obj, constraints)
In = np.array([7.09364830858073, 5.36952559622012, 0.305480348185421, 0.015403254279958, 0.639418852045523, 8.54820909414561, 6.36110970560502]) mu_hat.value = In[5:7] Sigma_hat.value = In[2:5] y.value = In[0:2] mu_hat1.value = np.array([In[5:7].T @ In[5:7]]) Sigma_hat1.value = np.array([In[2]In[2]+In[3]In[3], In[2]In[3]+In[3]In[4], In[3]In[3]+In[4]In[4]]) y1.value = np.array([In[0:2].T @ In[0:2]]) prob.solve(solver = cp.SCS, verbose = False) print("Optimal Value (SCS): ", prob.value, "solver time: ", prob.solver_stats.solve_time) prob.solve(solver = cp.MOSEK, verbose = False) print("Optimal Value (MOSEK): ", prob.value, "solver time: ", prob.solver_stats.solve_time)
In the cvxpy repository I was advised to increase the solver precision, but that didn't really help.