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@Utkarsh-Detha
Created November 5, 2021 09:35
MOSEK solver logs for illustrative least-squares and 2-norm problems
Problem
Name : Sum-of-squares
Objective sense : max
Type : CONIC (conic optimization problem)
Constraints : 5626
Cones : 1
Scalar variables : 6527
Matrix variables : 0
Integer variables : 0
Optimizer - threads : 8
Optimizer - solved problem : the dual
Optimizer - Constraints : 200
Optimizer - Cones : 1
Optimizer - Scalar variables : 465 conic : 107
Optimizer - Semi-definite variables: 0 scalarized : 0
Factor - setup time : 0.00 dense det. time : 0.00
Factor - ML order time : 0.00 GP order time : 0.00
Factor - nonzeros before factor : 6689 after factor : 6805
Factor - dense dim. : 0 flops : 4.41e+05
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 0.0e+00 3.6e+02 2.0e+00 0.00e+00 -1.000000000e+00 0.000000000e+00 1.0e+00 0.01
1 5.0e-08 1.1e+00 1.1e-01 -1.00e+00 4.960026469e+02 1.660020636e+02 3.0e-03 0.01
2 1.4e-08 2.9e-01 5.7e-02 -9.99e-01 2.387440435e+03 1.174714928e+03 8.2e-04 0.01
3 4.6e-09 1.0e-01 3.3e-02 -9.98e-01 1.124214900e+04 7.687603705e+03 2.8e-04 0.01
4 2.5e-09 3.5e-02 2.0e-02 -9.95e-01 4.667631344e+04 3.657669361e+04 9.8e-05 0.01
5 4.5e-09 1.9e-02 1.4e-02 -9.82e-01 8.903325500e+04 7.010582668e+04 5.2e-05 0.01
6 4.0e-09 1.2e-02 1.1e-02 -9.71e-01 4.832354936e+05 4.559769337e+05 3.5e-05 0.01
7 5.5e-08 1.7e-03 4.2e-03 -9.68e-01 3.072374301e+06 2.890515517e+06 4.9e-06 0.01
8 1.1e-06 9.5e-04 2.9e-03 -8.64e-01 8.289313029e+06 7.991216139e+06 2.7e-06 0.01
9 4.3e-07 4.4e-04 2.0e-03 -9.25e-01 8.626878505e+06 7.970892218e+06 1.2e-06 0.01
10 7.5e-07 2.9e-04 1.4e-03 -7.95e-01 3.305192666e+07 3.225377427e+07 8.0e-07 0.02
11 1.3e-06 6.7e-05 4.6e-04 -6.37e-01 1.301100655e+08 1.286101798e+08 1.9e-07 0.02
12 1.6e-05 1.9e-05 8.9e-05 2.57e-03 2.774563813e+08 2.767697848e+08 5.4e-08 0.02
13 3.2e-06 3.9e-06 5.0e-06 1.04e+00 3.569880554e+08 3.569349076e+08 1.1e-08 0.02
14 1.8e-04 8.7e-07 7.4e-07 1.47e+00 3.727958420e+08 3.727903994e+08 2.2e-09 0.02
15 1.1e-04 4.4e-07 8.2e-08 9.96e-01 3.738918735e+08 3.738891138e+08 1.1e-09 0.02
16 1.1e-04 4.3e-07 5.3e-08 9.99e-01 3.739307883e+08 3.739281148e+08 1.1e-09 0.02
17 1.1e-04 4.3e-07 5.3e-08 1.00e+00 3.739307883e+08 3.739281148e+08 1.1e-09 0.02
18 1.1e-04 4.3e-07 5.3e-08 1.00e+00 3.739307883e+08 3.739281148e+08 1.1e-09 0.02
19 5.6e-05 2.2e-07 2.1e-08 1.00e+00 3.745231585e+08 3.745218142e+08 5.2e-10 0.02
20 5.6e-05 2.2e-07 2.1e-08 1.00e+00 3.745231585e+08 3.745218142e+08 5.2e-10 0.02
21 5.6e-05 2.2e-07 2.1e-08 1.00e+00 3.745231585e+08 3.745218142e+08 5.2e-10 0.02
Optimizer terminated. Time: 0.02
Interior-point solution summary
Problem status : UNKNOWN
Solution status : UNKNOWN
Primal. obj: 3.7452315852e+08 nrm: 2e+08 Viol. con: 3e-10 var: 0e+00 cones: 0e+00
Dual. obj: 3.7452181420e+08 nrm: 4e+08 Viol. con: 0e+00 var: 6e+03 cones: 0e+00
Problem
Name : Euclidean-norm
Objective sense : max
Type : CONIC (conic optimization problem)
Constraints : 5626
Cones : 1
Scalar variables : 6526
Matrix variables : 0
Integer variables : 0
Optimizer - threads : 8
Optimizer - solved problem : the dual
Optimizer - Constraints : 199
Optimizer - Cones : 1
Optimizer - Scalar variables : 464 conic : 106
Optimizer - Semi-definite variables: 0 scalarized : 0
Factor - setup time : 0.00 dense det. time : 0.00
Factor - ML order time : 0.00 GP order time : 0.00
Factor - nonzeros before factor : 6584 after factor : 6700
Factor - dense dim. : 0 flops : 4.30e+05
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 0.0e+00 3.6e+02 2.0e+00 0.00e+00 0.000000000e+00 1.000000000e+00 1.0e+00 0.01
1 6.8e-09 4.2e+01 6.9e-01 -1.00e+00 1.501036940e+01 8.574572891e+00 1.2e-01 0.01
2 3.8e-09 2.4e+01 5.1e-01 -9.99e-01 6.279790020e+01 4.982675952e+01 6.7e-02 0.01
3 2.8e-09 1.7e+01 4.3e-01 -9.73e-01 3.024148977e+02 2.841987192e+02 4.8e-02 0.01
4 1.2e-09 7.2e+00 2.7e-01 -9.47e-01 1.403012164e+03 1.361535218e+03 2.0e-02 0.01
5 5.1e-10 3.2e+00 1.5e-01 -7.72e-01 4.375311681e+03 4.307120804e+03 8.9e-03 0.01
6 1.3e-10 8.4e-01 3.4e-02 -3.16e-01 1.285288466e+04 1.280108793e+04 2.3e-03 0.01
7 2.2e-11 1.3e-01 1.3e-03 8.77e-01 1.841713195e+04 1.841402952e+04 3.8e-04 0.01
8 3.3e-12 2.1e-02 5.4e-05 1.48e+00 1.926071277e+04 1.926050868e+04 5.8e-05 0.01
9 4.7e-13 2.9e-03 2.1e-06 1.38e+00 1.935907086e+04 1.935905559e+04 8.2e-06 0.01
10 5.0e-12 3.0e-04 5.8e-08 1.40e+00 1.937066316e+04 1.937066210e+04 8.4e-07 0.01
11 1.1e-12 5.9e-06 1.3e-10 1.16e+00 1.937169004e+04 1.937169003e+04 1.6e-08 0.01
12 1.5e-11 7.5e-10 6.6e-15 9.99e-01 1.937170752e+04 1.937170752e+04 1.0e-10 0.01
Optimizer terminated. Time: 0.02
Interior-point solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: 1.9371707520e+04 nrm: 3e+03 Viol. con: 7e-17 var: 1e-11 cones: 0e+00
Dual. obj: 1.9371707520e+04 nrm: 2e+04 Viol. con: 0e+00 var: 3e-04 cones: 3e-12
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