For K=4 is:
Calling Mosek 9.1.9: 64 variables, 20 equality constraints
For improved efficiency, Mosek is solving the dual problem.
MOSEK Version 9.1.9 (Build date: 2019-11-21 11:34:40)
Copyright © MOSEK ApS, Denmark. WWW: mosek.com
Platform: Windows/64-X86
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 20
Cones : 8
Scalar variables : 64
Matrix variables : 0
Integer variables : 0
Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 12
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
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 20
Cones : 8
Scalar variables : 64
Matrix variables : 0
Integer variables : 0
Optimizer - threads : 2
Optimizer - solved problem : the primal
Optimizer - Constraints : 8
Optimizer - Cones : 8
Optimizer - Scalar variables : 37 conic : 24
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 : 30 after factor : 36
Factor - dense dim. : 0 flops : 1.21e+03
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 2.1e+03 1.0e+00 5.0e+00 0.00e+00 3.999999999e+00 0.000000000e+00 1.0e+00 0.03
1 4.2e+02 2.1e-01 2.3e+00 -1.00e+00 3.489184090e+01 3.475514166e+01 2.1e-01 0.11
2 6.4e+00 3.1e-03 2.7e-01 -9.99e-01 2.456907881e+03 2.759602904e+03 3.1e-03 0.11
3 2.5e+00 1.2e-03 1.1e-01 -6.29e-01 2.961566040e+03 3.289942369e+03 1.2e-03 0.13
4 7.2e-01 3.5e-04 6.6e-03 8.91e-01 3.687174249e+02 3.821668227e+02 3.5e-04 0.13
5 1.5e-02 7.2e-06 1.5e-05 8.82e-01 1.349584536e+01 1.366382578e+01 7.2e-06 0.13
6 1.5e-03 7.3e-07 5.0e-07 9.97e-01 1.121759579e+00 1.139418848e+00 7.3e-07 0.13
7 3.7e-04 1.8e-07 8.4e-08 9.44e-01 2.028347410e-01 2.112164291e-01 1.8e-07 0.13
8 1.6e-04 7.6e-08 4.2e-08 6.14e-01 -5.611895934e-03 6.162667195e-03 7.6e-08 0.14
9 5.0e-05 2.5e-08 4.1e-08 -5.69e-01 3.851600474e-02 1.506923689e-01 2.5e-08 0.14
10 4.2e-07 2.0e-10 3.0e-09 -8.70e-01 -8.648531627e+00 -2.043526746e-02 2.0e-10 0.14
11 9.2e-12 6.0e-16 4.9e-12 -1.00e+00 -4.314686594e+06 -5.007240355e-03 6.0e-16 0.14
12 6.7e-12 7.7e-26 1.2e-06 -1.00e+00 -4.797211025e+17 5.887369227e-02 5.4e-27 0.14
13 4.4e-16 2.0e-34 6.3e-07 -1.00e+00 -2.277260209e-05 1.856546390e-36 3.3e-38 0.16
Optimizer terminated. Time: 0.19
Interior-point solution summary
Problem status : DUAL_INFEASIBLE
Solution status : DUAL_INFEASIBLE_CER
Primal. obj: -2.2772602094e-05 nrm: 5e+00 Viol. con: 1e-16 var: 0e+00 cones: 0e+00
Optimizer summary
Optimizer - time: 0.19
Interior-point - iterations : 13 time: 0.16
Basis identification - time: 0.00
Primal - iterations : 0 time: 0.00
Dual - iterations : 0 time: 0.00
Clean primal - iterations : 0 time: 0.00
Clean dual - iterations : 0 time: 0.00
Simplex - time: 0.00
Primal simplex - iterations : 0 time: 0.00
Dual simplex - iterations : 0 time: 0.00
Mixed integer - relaxations: 0 time: 0.00
Status: Infeasible
Optimal value (cvx_optval): +Inf
Calling Mosek 9.1.9: 64 variables, 20 equality constraints
For improved efficiency, Mosek is solving the dual problem.
MOSEK Version 9.1.9 (Build date: 2019-11-21 11:34:40)
Copyright © MOSEK ApS, Denmark. WWW: mosek.com
Platform: Windows/64-X86
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 20
Cones : 8
Scalar variables : 64
Matrix variables : 0
Integer variables : 0
Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 12
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: 0.02
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 20
Cones : 8
Scalar variables : 64
Matrix variables : 0
Integer variables : 0
Optimizer - threads : 2
Optimizer - solved problem : the primal
Optimizer - Constraints : 8
Optimizer - Cones : 8
Optimizer - Scalar variables : 38 conic : 24
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 : 30 after factor : 36
Factor - dense dim. : 0 flops : 1.23e+03
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 2.0e+03 1.0e+00 5.0e+00 0.00e+00 3.999999999e+00 0.000000000e+00 1.0e+00 0.03
1 2.0e+02 1.0e-01 1.6e+00 -1.00e+00 7.647890192e+01 8.152497775e+01 1.0e-01 0.11
2 1.2e+01 6.1e-03 4.0e-01 -1.01e+00 1.389113443e+03 1.558307536e+03 6.1e-03 0.11
3 4.2e+00 2.1e-03 2.0e-01 -9.39e-01 3.013145455e+03 3.375630931e+03 2.1e-03 0.11
4 1.2e+00 6.0e-04 1.7e-02 2.65e-01 7.699566843e+02 7.997409709e+02 6.0e-04 0.13
5 4.4e-02 2.2e-05 1.2e-04 8.52e-01 4.599406013e+01 4.710424765e+01 2.2e-05 0.13
6 2.0e-03 9.5e-07 1.1e-06 1.01e+00 1.756029215e+00 1.805799525e+00 9.5e-07 0.13
7 5.4e-04 2.6e-07 1.8e-07 9.64e-01 3.941271448e-01 4.127584396e-01 2.6e-07 0.13
8 2.3e-04 1.1e-07 8.4e-08 6.93e-01 9.719110882e-02 1.181670109e-01 1.1e-07 0.13
9 7.9e-05 3.9e-08 4.8e-08 2.10e-02 -6.674364447e-02 -6.106879691e-03 3.9e-08 0.14
10 7.9e-06 3.8e-09 2.1e-08 -7.69e-01 -9.173839321e-01 2.943215900e-01 3.8e-09 0.14
11 6.6e-09 3.2e-12 6.7e-10 -9.71e-01 -1.695090715e+03 2.153842909e-01 3.2e-12 0.14
12 1.3e-12 2.4e-21 2.3e-09 -1.00e+00 -3.333588670e+12 2.815891528e-01 2.1e-21 0.14
13 6.1e-16 5.7e-29 6.3e-10 -1.00e+00 -3.354470605e-05 2.151783749e-29 1.5e-32 0.14
Optimizer terminated. Time: 0.20
Interior-point solution summary
Problem status : DUAL_INFEASIBLE
Solution status : DUAL_INFEASIBLE_CER
Primal. obj: -3.3544706051e-05 nrm: 5e+00 Viol. con: 4e-16 var: 0e+00 cones: 0e+00
Optimizer summary
Optimizer - time: 0.20
Interior-point - iterations : 13 time: 0.16
Basis identification - time: 0.00
Primal - iterations : 0 time: 0.00
Dual - iterations : 0 time: 0.00
Clean primal - iterations : 0 time: 0.00
Clean dual - iterations : 0 time: 0.00
Simplex - time: 0.00
Primal simplex - iterations : 0 time: 0.00
Dual simplex - iterations : 0 time: 0.00
Mixed integer - relaxations: 0 time: 0.00
Status: Infeasible
Optimal value (cvx_optval): +Inf
Calling Mosek 9.1.9: 64 variables, 20 equality constraints
For improved efficiency, Mosek is solving the dual problem.
MOSEK Version 9.1.9 (Build date: 2019-11-21 11:34:40)
Copyright © MOSEK ApS, Denmark. WWW: mosek.com
Platform: Windows/64-X86
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 20
Cones : 8
Scalar variables : 64
Matrix variables : 0
Integer variables : 0
Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 12
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
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 20
Cones : 8
Scalar variables : 64
Matrix variables : 0
Integer variables : 0
Optimizer - threads : 2
Optimizer - solved problem : the primal
Optimizer - Constraints : 8
Optimizer - Cones : 8
Optimizer - Scalar variables : 39 conic : 24
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 : 30 after factor : 36
Factor - dense dim. : 0 flops : 1.25e+03
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 4.1e+03 1.0e+00 5.0e+00 0.00e+00 3.999999999e+00 0.000000000e+00 1.0e+00 0.03
1 8.9e+02 2.2e-01 2.3e+00 -1.00e+00 3.289314572e+01 3.250431342e+01 2.2e-01 0.11
2 3.2e+01 7.7e-03 4.4e-01 -1.00e+00 1.038433273e+03 1.163726966e+03 7.7e-03 0.11
3 5.9e+00 1.4e-03 1.8e-01 -9.89e-01 5.159805696e+03 5.797832473e+03 1.4e-03 0.13
4 4.6e+00 1.1e-03 1.2e-01 -2.98e-01 4.212379401e+03 4.693849001e+03 1.1e-03 0.13
5 1.1e+00 2.6e-04 1.0e-02 1.61e-01 1.340794765e+03 1.405991232e+03 2.6e-04 0.13
6 2.9e-02 7.1e-06 2.8e-05 1.04e+00 2.540933978e+01 2.601387180e+01 7.1e-06 0.13
7 1.1e-03 2.6e-07 2.0e-07 9.92e-01 7.271565039e-01 7.514993923e-01 2.6e-07 0.13
8 2.9e-04 7.1e-08 4.4e-08 7.83e-01 1.073151128e-01 1.224259516e-01 7.1e-08 0.14
9 1.1e-04 2.6e-08 2.7e-08 1.39e-01 -2.316431313e-01 -1.902874990e-01 2.6e-08 0.14
10 3.1e-05 7.5e-09 2.7e-08 -1.11e+00 -1.044117911e-01 4.085748749e-01 7.5e-09 0.14
11 3.3e-07 7.9e-11 3.2e-09 -9.30e-01 -6.440088417e+01 1.404938297e-01 7.9e-11 0.14
12 7.1e-12 1.4e-16 3.5e-12 -1.00e+00 -4.848553654e+07 9.543055920e-02 1.4e-16 0.14
13 8.9e-16 3.0e-22 1.2e-13 -1.00e+00 -2.798119361e-05 -7.418926886e-22 6.4e-26 0.16
Optimizer terminated. Time: 0.19
Interior-point solution summary
Problem status : DUAL_INFEASIBLE
Solution status : DUAL_INFEASIBLE_CER
Primal. obj: -2.7981193614e-05 nrm: 4e+00 Viol. con: 9e-16 var: 0e+00 cones: 0e+00
Optimizer summary
Optimizer - time: 0.19
Interior-point - iterations : 13 time: 0.16
Basis identification - time: 0.00
Primal - iterations : 0 time: 0.00
Dual - iterations : 0 time: 0.00
Clean primal - iterations : 0 time: 0.00
Clean dual - iterations : 0 time: 0.00
Simplex - time: 0.00
Primal simplex - iterations : 0 time: 0.00
Dual simplex - iterations : 0 time: 0.00
Mixed integer - relaxations: 0 time: 0.00
Status: Infeasible
Optimal value (cvx_optval): +Inf
Calling Mosek 9.1.9: 64 variables, 20 equality constraints
For improved efficiency, Mosek is solving the dual problem.
MOSEK Version 9.1.9 (Build date: 2019-11-21 11:34:40)
Copyright © MOSEK ApS, Denmark. WWW: mosek.com
Platform: Windows/64-X86
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 20
Cones : 8
Scalar variables : 64
Matrix variables : 0
Integer variables : 0
Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 12
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: 0.03
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 20
Cones : 8
Scalar variables : 64
Matrix variables : 0
Integer variables : 0
Optimizer - threads : 2
Optimizer - solved problem : the primal
Optimizer - Constraints : 8
Optimizer - Cones : 8
Optimizer - Scalar variables : 39 conic : 24
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 : 30 after factor : 36
Factor - dense dim. : 0 flops : 1.25e+03
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 2.0e+03 1.0e+00 5.0e+00 0.00e+00 3.999999999e+00 0.000000000e+00 1.0e+00 0.05
1 4.7e+02 2.3e-01 2.4e+00 -1.00e+00 3.090231028e+01 3.026664741e+01 2.3e-01 0.11
2 2.7e+01 1.3e-02 5.7e-01 -9.99e-01 6.042820253e+02 6.753280293e+02 1.3e-02 0.13
3 5.7e+00 2.8e-03 2.4e-01 -9.63e-01 2.494849957e+03 2.799521293e+03 2.8e-03 0.13
4 2.0e+00 9.6e-04 4.8e-02 -1.87e-01 1.232604933e+03 1.328474929e+03 9.6e-04 0.13
5 1.8e-01 8.7e-05 6.4e-04 9.59e-01 7.631945957e+01 7.830488723e+01 8.7e-05 0.13
6 2.3e-03 1.1e-06 9.3e-07 9.95e-01 7.712125581e-01 7.966768361e-01 1.1e-06 0.13
7 4.9e-04 2.4e-07 1.2e-07 9.24e-01 8.373087182e-02 9.271771266e-02 2.4e-07 0.14
8 1.7e-04 8.4e-08 5.1e-08 5.01e-01 -5.303744824e-02 -3.864991414e-02 8.4e-08 0.14
9 6.6e-05 3.2e-08 5.9e-08 -7.18e-01 -6.373066057e-02 6.807796958e-02 3.2e-08 0.14
10 3.3e-06 1.6e-09 1.5e-08 -9.14e-01 -3.295441664e+00 2.778770100e-02 1.6e-09 0.14
11 6.0e-10 2.9e-13 2.1e-10 -9.99e-01 -2.160862517e+04 2.240251523e-02 2.9e-13 0.14
12 6.0e-12 2.9e-17 7.2e-12 -1.00e+00 -2.160864524e+08 2.240251404e-02 2.9e-17 0.14
13 4.4e-16 8.8e-24 5.3e-12 -1.00e+00 -2.973626571e-05 -6.295271740e-24 1.5e-27 0.16
Optimizer terminated. Time: 0.19
Interior-point solution summary
Problem status : DUAL_INFEASIBLE
Solution status : DUAL_INFEASIBLE_CER
Primal. obj: -2.9736265708e-05 nrm: 5e+00 Viol. con: 4e-16 var: 0e+00 cones: 0e+00
Optimizer summary
Optimizer - time: 0.19
Interior-point - iterations : 13 time: 0.16
Basis identification - time: 0.00
Primal - iterations : 0 time: 0.00
Dual - iterations : 0 time: 0.00
Clean primal - iterations : 0 time: 0.00
Clean dual - iterations : 0 time: 0.00
Simplex - time: 0.00
Primal simplex - iterations : 0 time: 0.00
Dual simplex - iterations : 0 time: 0.00
Mixed integer - relaxations: 0 time: 0.00
Status: Infeasible
Optimal value (cvx_optval): +Inf
Calling Mosek 9.1.9: 64 variables, 20 equality constraints
For improved efficiency, Mosek is solving the dual problem.
MOSEK Version 9.1.9 (Build date: 2019-11-21 11:34:40)
Copyright © MOSEK ApS, Denmark. WWW: mosek.com
Platform: Windows/64-X86
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 20
Cones : 8
Scalar variables : 64
Matrix variables : 0
Integer variables : 0
Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 12
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: 0.03
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 20
Cones : 8
Scalar variables : 64
Matrix variables : 0
Integer variables : 0
Optimizer - threads : 2
Optimizer - solved problem : the primal
Optimizer - Constraints : 8
Optimizer - Cones : 8
Optimizer - Scalar variables : 37 conic : 24
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 : 30 after factor : 36
Factor - dense dim. : 0 flops : 1.21e+03
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 4.1e+03 1.0e+00 5.0e+00 0.00e+00 3.999999999e+00 0.000000000e+00 1.0e+00 0.05
1 7.4e+02 1.8e-01 2.1e+00 -1.00e+00 4.021455501e+01 4.074104643e+01 1.8e-01 0.13
2 8.8e+00 2.1e-03 2.3e-01 -1.00e+00 3.824882888e+03 4.298446759e+03 2.1e-03 0.13
3 5.1e+00 1.2e-03 1.2e-01 -5.77e-01 3.197312157e+03 3.543528450e+03 1.2e-03 0.14
4 9.1e-01 2.2e-04 4.8e-03 3.14e-01 7.285668954e+02 7.466560613e+02 2.2e-04 0.14
5 6.1e-03 1.5e-06 3.7e-06 1.04e+00 1.614259897e+00 1.862345493e+00 1.5e-06 0.14
6 1.0e-03 2.4e-07 2.7e-07 9.68e-01 5.599521465e-02 1.030623332e-01 2.4e-07 0.14
7 3.2e-04 7.8e-08 6.1e-08 8.06e-01 -1.205951131e-01 -9.601444103e-02 7.8e-08 0.14
8 1.3e-04 3.2e-08 4.8e-08 -1.95e-02 -3.479457240e-01 -2.578208521e-01 3.2e-08 0.16
9 1.5e-05 3.8e-09 2.3e-08 -1.12e+00 -1.660984157e+00 -1.108089176e-01 3.8e-09 0.16
10 3.5e-08 8.6e-12 1.3e-09 -9.97e-01 -9.491586013e+02 -8.309536659e-02 8.6e-12 0.16
11 3.1e-12 7.3e-20 6.2e-10 -1.00e+00 -1.558862304e+11 -4.713933300e-02 7.2e-20 0.16
12 1.3e-12 2.4e-30 2.3e-04 -1.00e+00 -3.666626817e+22 -1.943671060e-01 2.6e-31 0.16
13 2.2e-16 5.7e-39 1.2e-04 -1.00e+00 -4.145173052e-05 -7.907352072e-40 1.5e-42 0.17
Optimizer terminated. Time: 0.19
Interior-point solution summary
Problem status : DUAL_INFEASIBLE
Solution status : DUAL_INFEASIBLE_CER
Primal. obj: -4.1451730523e-05 nrm: 7e+00 Viol. con: 4e-16 var: 0e+00 cones: 0e+00
Optimizer summary
Optimizer - time: 0.19
Interior-point - iterations : 13 time: 0.17
Basis identification - time: 0.00
Primal - iterations : 0 time: 0.00
Dual - iterations : 0 time: 0.00
Clean primal - iterations : 0 time: 0.00
Clean dual - iterations : 0 time: 0.00
Simplex - time: 0.00
Primal simplex - iterations : 0 time: 0.00
Dual simplex - iterations : 0 time: 0.00
Mixed integer - relaxations: 0 time: 0.00
Status: Infeasible
Optimal value (cvx_optval): +Inf
opt_finded =
NaN