MOSEK solver logs for illustrative least-squares and 2-norm problems

leastsq_log.txt

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

norm_log.txt

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