MOSEK Version 9.1.9 (Build date: 2019-11-21 11:32:15)
Copyright © MOSEK ApS, Denmark. WWW: mosek.com
Platform: MACOSX/64-X86
MOSEK warning 710: #2 (nearly) zero elements are specified in sparse col ‘’ (3) of matrix ‘A’.
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 173
Cones : 12
Scalar variables : 67
Matrix variables : 8
Integer variables : 0
Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 0
Eliminator terminated.
Eliminator - tries : 1 time : 0.00
Lin. dep. - tries : 1 time : 0.00
Lin. dep. - number : 0
Presolve terminated. Time: 0.00
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 173
Cones : 12
Scalar variables : 67
Matrix variables : 8
Integer variables : 0
Optimizer - threads : 10
Optimizer - solved problem : the primal
Optimizer - Constraints : 159
Optimizer - Cones : 12
Optimizer - Scalar variables : 54 conic : 36
Optimizer - Semi-definite variables: 8 scalarized : 624
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 : 1.20e+04 after factor : 1.20e+04
Factor - dense dim. : 0 flops : 1.69e+06
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 4.0e+00 5.0e+00 7.7e+00 0.00e+00 6.676676123e+00 0.000000000e+00 1.0e+00 0.00
1 2.5e+00 3.0e+00 2.6e+00 1.64e+00 3.987814089e+00 8.903021226e-01 6.1e-01 0.00
2 9.4e-01 1.2e+00 4.8e-01 1.32e+00 3.009347205e+00 2.019609236e+00 2.4e-01 0.01
3 4.6e-01 5.7e-01 2.2e-01 8.30e-01 4.083170216e+00 3.490075683e+00 1.1e-01 0.01
4 1.5e-01 1.9e-01 4.8e-02 8.34e-01 4.177187176e+00 3.958647385e+00 3.8e-02 0.01
5 6.5e-02 8.1e-02 2.3e-02 3.83e-01 5.349242874e+00 5.196754277e+00 1.6e-02 0.01
6 2.6e-02 3.2e-02 6.9e-03 5.35e-01 5.607585775e+00 5.537071821e+00 6.4e-03 0.01
7 1.2e-02 1.5e-02 3.3e-03 2.67e-01 6.211376293e+00 6.166892214e+00 3.0e-03 0.01
8 3.2e-03 4.0e-03 8.9e-04 1.73e-01 7.226465511e+00 7.214983483e+00 8.0e-04 0.01
9 1.4e-03 1.7e-03 3.4e-04 2.74e-01 7.634804695e+00 7.631721455e+00 3.5e-04 0.01
10 4.1e-04 5.1e-04 1.1e-04 8.15e-02 8.626163574e+00 8.634243373e+00 1.0e-04 0.02
11 1.7e-04 2.1e-04 4.6e-05 6.09e-02 9.224399513e+00 9.237269340e+00 4.2e-05 0.02
12 5.0e-05 6.2e-05 1.2e-05 1.56e-01 9.845716425e+00 9.857484887e+00 1.2e-05 0.02
13 1.7e-05 2.1e-05 4.6e-06 4.01e-02 1.078705580e+01 1.080458605e+01 4.3e-06 0.02
14 4.8e-06 5.9e-06 1.1e-06 2.16e-01 1.146394235e+01 1.147704455e+01 1.2e-06 0.02
15 1.6e-06 1.9e-06 4.4e-07 4.83e-02 1.264458865e+01 1.266510988e+01 3.9e-07 0.02
16 4.6e-07 5.7e-07 9.5e-08 3.47e-01 1.309687323e+01 1.310807842e+01 1.1e-07 0.02
17 1.6e-07 2.0e-07 2.9e-08 3.02e-01 1.358965043e+01 1.359824982e+01 4.1e-08 0.02
18 6.4e-08 7.9e-08 7.9e-09 5.62e-01 1.365602227e+01 1.366018643e+01 1.6e-08 0.03
19 3.0e-08 3.7e-08 2.5e-09 8.95e-01 1.365740109e+01 1.365934817e+01 7.5e-09 0.03
20 2.0e-08 2.4e-08 1.4e-09 1.03e+00 1.365419319e+01 1.365545430e+01 4.9e-09 0.03
21 7.2e-09 8.8e-09 2.9e-10 1.08e+00 1.366002980e+01 1.366046052e+01 1.8e-09 0.03
22 3.5e-09 4.3e-09 9.5e-11 1.12e+00 1.366077194e+01 1.366097314e+01 8.7e-10 0.03
23 9.5e-10 1.2e-09 1.3e-11 1.09e+00 1.366354365e+01 1.366359573e+01 2.4e-10 0.03
24 2.4e-10 3.0e-10 1.7e-12 1.06e+00 1.366490555e+01 1.366491875e+01 6.0e-11 0.04
25 2.4e-10 3.0e-10 1.7e-12 1.04e+00 1.366490570e+01 1.366491889e+01 6.0e-11 0.04
26 2.4e-10 3.0e-10 1.7e-12 1.04e+00 1.366490686e+01 1.366492001e+01 6.0e-11 0.04
27 4.9e-11 6.0e-11 1.5e-13 1.04e+00 1.366519871e+01 1.366520126e+01 1.2e-11 0.05
28 6.9e-11 6.0e-11 1.5e-13 1.00e+00 1.366519942e+01 1.366520195e+01 1.2e-11 0.05
29 8.0e-11 5.9e-11 1.5e-13 9.99e-01 1.366520014e+01 1.366520265e+01 1.2e-11 0.05
30 8.0e-11 5.9e-11 1.5e-13 1.00e+00 1.366520031e+01 1.366520282e+01 1.2e-11 0.06
31 7.5e-11 5.9e-11 1.5e-13 1.01e+00 1.366520040e+01 1.366520290e+01 1.2e-11 0.06
32 7.9e-11 5.9e-11 1.5e-13 9.57e-01 1.366520049e+01 1.366520299e+01 1.2e-11 0.06
33 8.0e-11 5.8e-11 1.4e-13 9.92e-01 1.366520191e+01 1.366520438e+01 1.2e-11 0.07
34 8.0e-11 5.8e-11 1.4e-13 9.96e-01 1.366520193e+01 1.366520440e+01 1.2e-11 0.07
35 8.0e-11 5.8e-11 1.4e-13 9.99e-01 1.366520197e+01 1.366520444e+01 1.2e-11 0.07
36 7.8e-11 5.8e-11 1.4e-13 1.01e+00 1.366520215e+01 1.366520461e+01 1.2e-11 0.08
37 8.0e-11 5.8e-11 1.4e-13 9.99e-01 1.366520232e+01 1.366520478e+01 1.2e-11 0.08
38 8.0e-11 5.8e-11 1.4e-13 1.00e+00 1.366520267e+01 1.366520512e+01 1.2e-11 0.08
39 8.0e-11 5.8e-11 1.4e-13 1.00e+00 1.366520267e+01 1.366520512e+01 1.2e-11 0.09
40 8.0e-11 5.8e-11 1.4e-13 1.00e+00 1.366520267e+01 1.366520512e+01 1.2e-11 0.09
41 7.8e-11 5.6e-11 1.4e-13 9.99e-01 1.366520543e+01 1.366520782e+01 1.1e-11 0.09
42 8.0e-11 5.6e-11 1.3e-13 9.99e-01 1.366520611e+01 1.366520847e+01 1.1e-11 0.10
43 8.0e-11 5.0e-11 1.1e-13 9.97e-01 1.366521681e+01 1.366521891e+01 1.0e-11 0.10
44 8.0e-11 5.0e-11 1.1e-13 1.00e+00 1.366521688e+01 1.366521899e+01 1.0e-11 0.10
45 7.5e-11 4.7e-11 1.0e-13 1.01e+00 1.366522170e+01 1.366522368e+01 9.4e-12 0.11
46 7.7e-11 4.2e-11 8.6e-14 9.99e-01 1.366523082e+01 1.366523258e+01 8.4e-12 0.11
47 8.0e-11 4.0e-11 8.3e-14 1.00e+00 1.366523286e+01 1.366523458e+01 8.1e-12 0.11
48 8.0e-11 4.0e-11 8.2e-14 1.00e+00 1.366523336e+01 1.366523506e+01 8.1e-12 0.12
49 8.0e-11 4.0e-11 8.2e-14 1.00e+00 1.366523339e+01 1.366523509e+01 8.1e-12 0.12
50 8.0e-11 4.0e-11 8.2e-14 1.00e+00 1.366523342e+01 1.366523512e+01 8.1e-12 0.13
51 8.0e-11 4.0e-11 8.2e-14 1.00e+00 1.366523343e+01 1.366523513e+01 8.1e-12 0.13
52 8.0e-11 3.8e-11 7.5e-14 1.00e+00 1.366523739e+01 1.366523899e+01 7.6e-12 0.13
53 8.0e-11 3.6e-11 6.8e-14 1.00e+00 1.366524114e+01 1.366524265e+01 7.2e-12 0.14
54 7.6e-11 3.5e-11 6.5e-14 1.00e+00 1.366524292e+01 1.366524439e+01 6.9e-12 0.14
55 7.9e-11 2.7e-11 4.4e-14 1.00e+00 1.366525677e+01 1.366525790e+01 5.3e-12 0.14
56 8.0e-11 2.6e-11 4.3e-14 1.00e+00 1.366525745e+01 1.366525856e+01 5.3e-12 0.15
57 7.9e-11 2.3e-11 3.6e-14 1.00e+00 1.366526279e+01 1.366526377e+01 4.6e-12 0.15
58 8.0e-11 2.3e-11 3.5e-14 1.00e+00 1.366526338e+01 1.366526435e+01 4.6e-12 0.15
59 8.0e-11 2.2e-11 3.4e-14 1.00e+00 1.366526397e+01 1.366526492e+01 4.5e-12 0.15
60 8.0e-11 2.2e-11 3.4e-14 1.00e+00 1.366526426e+01 1.366526520e+01 4.5e-12 0.16
61 7.6e-11 2.0e-11 2.8e-14 1.00e+00 1.366526884e+01 1.366526967e+01 3.9e-12 0.16
62 8.0e-11 1.8e-11 2.6e-14 1.00e+00 1.366527087e+01 1.366527165e+01 3.7e-12 0.17
63 7.8e-11 1.8e-11 2.6e-14 1.35e+00 1.366527088e+01 1.366527167e+01 3.7e-12 0.17
64 7.7e-11 1.7e-11 2.3e-14 1.00e+00 1.366527280e+01 1.366527353e+01 3.5e-12 0.17
65 8.0e-11 1.5e-11 1.9e-14 1.00e+00 1.366527640e+01 1.366527705e+01 3.1e-12 0.18
66 7.2e-11 1.3e-11 1.6e-14 1.00e+00 1.366527958e+01 1.366528015e+01 2.7e-12 0.18
67 7.6e-11 1.3e-11 1.5e-14 1.00e+00 1.366528029e+01 1.366528084e+01 2.6e-12 0.18
68 7.9e-11 1.3e-11 1.5e-14 1.00e+00 1.366528063e+01 1.366528117e+01 2.6e-12 0.19
69 8.0e-11 1.3e-11 1.5e-14 1.00e+00 1.366528096e+01 1.366528150e+01 2.5e-12 0.19
70 7.8e-11 1.2e-11 1.4e-14 1.00e+00 1.366528129e+01 1.366528182e+01 2.5e-12 0.19
71 8.0e-11 1.2e-11 1.4e-14 1.00e+00 1.366528146e+01 1.366528198e+01 2.5e-12 0.20
72 7.9e-11 1.2e-11 1.4e-14 1.00e+00 1.366528178e+01 1.366528230e+01 2.4e-12 0.20
73 8.0e-11 1.2e-11 1.4e-14 1.00e+00 1.366528194e+01 1.366528246e+01 2.4e-12 0.20
74 7.9e-11 1.1e-11 1.1e-14 1.00e+00 1.366528448e+01 1.366528493e+01 2.1e-12 0.20
75 8.0e-11 1.0e-11 1.1e-14 1.00e+00 1.366528475e+01 1.366528520e+01 2.1e-12 0.21
76 8.0e-11 1.0e-11 1.1e-14 1.00e+00 1.366528479e+01 1.366528523e+01 2.1e-12 0.21
77 8.0e-11 1.0e-11 1.1e-14 1.00e+00 1.366528506e+01 1.366528550e+01 2.1e-12 0.21
78 8.0e-11 1.0e-11 1.1e-14 1.00e+00 1.366528507e+01 1.366528551e+01 2.1e-12 0.22
79 8.0e-11 1.0e-11 1.1e-14 1.00e+00 1.366528507e+01 1.366528551e+01 2.1e-12 0.22
80 8.1e-11 1.0e-11 1.1e-14 1.00e+00 1.366528507e+01 1.366528551e+01 2.1e-12 0.23
81 8.1e-11 1.0e-11 1.1e-14 1.00e+00 1.366528507e+01 1.366528551e+01 2.1e-12 0.23
82 8.1e-11 1.0e-11 1.1e-14 1.05e+00 1.366528507e+01 1.366528551e+01 2.1e-12 0.24
83 8.0e-11 1.0e-11 1.1e-14 1.00e+00 1.366528509e+01 1.366528553e+01 2.1e-12 0.24
84 7.8e-11 1.0e-11 1.1e-14 1.00e+00 1.366528510e+01 1.366528554e+01 2.1e-12 0.24
85 8.0e-11 1.0e-11 1.1e-14 1.00e+00 1.366528510e+01 1.366528554e+01 2.1e-12 0.25
86 8.0e-11 1.0e-11 1.1e-14 1.00e+00 1.366528511e+01 1.366528555e+01 2.1e-12 0.25
87 7.8e-11 1.0e-11 1.1e-14 1.00e+00 1.366528513e+01 1.366528556e+01 2.0e-12 0.26
88 7.7e-11 1.0e-11 1.1e-14 1.00e+00 1.366528514e+01 1.366528557e+01 2.0e-12 0.26
89 7.8e-11 1.0e-11 1.1e-14 1.00e+00 1.366528515e+01 1.366528558e+01 2.0e-12 0.26
90 8.0e-11 1.0e-11 1.1e-14 1.00e+00 1.366528515e+01 1.366528558e+01 2.0e-12 0.27
91 7.9e-11 1.0e-11 1.1e-14 1.00e+00 1.366528515e+01 1.366528559e+01 2.0e-12 0.27
92 8.0e-11 1.0e-11 1.1e-14 1.00e+00 1.366528516e+01 1.366528559e+01 2.0e-12 0.27
93 7.9e-11 1.0e-11 1.1e-14 1.00e+00 1.366528516e+01 1.366528559e+01 2.0e-12 0.28
94 7.4e-11 1.0e-11 1.1e-14 1.00e+00 1.366528518e+01 1.366528562e+01 2.0e-12 0.28
95 7.9e-11 1.0e-11 1.1e-14 1.00e+00 1.366528519e+01 1.366528563e+01 2.0e-12 0.28
96 8.0e-11 1.0e-11 1.1e-14 1.00e+00 1.366528520e+01 1.366528563e+01 2.0e-12 0.29
97 8.0e-11 1.0e-11 1.0e-14 1.00e+00 1.366528520e+01 1.366528563e+01 2.0e-12 0.29
98 8.0e-11 1.0e-11 1.0e-14 1.00e+00 1.366528520e+01 1.366528564e+01 2.0e-12 0.29
99 8.0e-11 1.0e-11 1.0e-14 1.00e+00 1.366528520e+01 1.366528564e+01 2.0e-12 0.30
100 8.0e-11 1.0e-11 1.0e-14 1.00e+00 1.366528530e+01 1.366528573e+01 2.0e-12 0.30
101 8.0e-11 1.0e-11 1.0e-14 1.00e+00 1.366528531e+01 1.366528574e+01 2.0e-12 0.30
102 8.0e-11 1.0e-11 1.0e-14 1.00e+00 1.366528531e+01 1.366528574e+01 2.0e-12 0.31
103 8.0e-11 1.0e-11 1.0e-14 1.00e+00 1.366528531e+01 1.366528574e+01 2.0e-12 0.31
104 8.0e-11 1.0e-11 1.0e-14 1.00e+00 1.366528531e+01 1.366528574e+01 2.0e-12 0.31
Optimizer terminated. Time: 0.32
Interior-point solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: 1.3665285307e+01 nrm: 3e+07 Viol. con: 4e-04 var: 0e+00 barvar: 0e+00 cones: 1e-09
Dual. obj: 1.3665285737e+01 nrm: 3e+04 Viol. con: 0e+00 var: 1e-09 barvar: 1e-09 cones: 0e+00
Optimizer summary
Optimizer - time: 0.32
Interior-point - iterations : 105 time: 0.32
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: Solved
Optimal value (cvx_optval): +13.6653
ans =
1.1390
Calling Mosek 9.1.9: 355 variables, 173 equality constraints
For improved efficiency, Mosek is solving the dual problem.
MOSEK Version 9.1.9 (Build date: 2019-11-21 11:32:15)
Copyright © MOSEK ApS, Denmark. WWW: mosek.com
Platform: MACOSX/64-X86
MOSEK warning 710: #2 (nearly) zero elements are specified in sparse col ‘’ (3) of matrix ‘A’.
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 173
Cones : 12
Scalar variables : 67
Matrix variables : 8
Integer variables : 0
Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 0
Eliminator terminated.
Eliminator - tries : 1 time : 0.00
Lin. dep. - tries : 1 time : 0.00
Lin. dep. - number : 0
Presolve terminated. Time: 0.00
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 173
Cones : 12
Scalar variables : 67
Matrix variables : 8
Integer variables : 0
Optimizer - threads : 10
Optimizer - solved problem : the primal
Optimizer - Constraints : 159
Optimizer - Cones : 12
Optimizer - Scalar variables : 54 conic : 36
Optimizer - Semi-definite variables: 8 scalarized : 624
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 : 1.20e+04 after factor : 1.20e+04
Factor - dense dim. : 0 flops : 1.69e+06
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 4.0e+00 5.0e+00 7.9e+00 0.00e+00 6.873696318e+00 0.000000000e+00 1.0e+00 0.00
1 2.5e+00 3.0e+00 2.7e+00 1.64e+00 4.090362462e+00 9.050795324e-01 6.1e-01 0.00
2 9.2e-01 1.1e+00 4.8e-01 1.32e+00 3.051261884e+00 2.059365059e+00 2.3e-01 0.01
3 4.7e-01 5.8e-01 2.3e-01 7.98e-01 4.201826683e+00 3.565613295e+00 1.2e-01 0.01
4 1.5e-01 1.8e-01 4.8e-02 8.44e-01 4.234423548e+00 4.011909751e+00 3.7e-02 0.01
5 6.4e-02 7.9e-02 2.3e-02 3.84e-01 5.393357038e+00 5.237926189e+00 1.6e-02 0.01
6 2.5e-02 3.1e-02 6.8e-03 5.33e-01 5.650893568e+00 5.579566891e+00 6.2e-03 0.01
7 1.2e-02 1.4e-02 3.4e-03 2.29e-01 6.324107266e+00 6.277482188e+00 2.9e-03 0.01
8 3.8e-03 4.7e-03 1.1e-03 2.11e-01 7.073357081e+00 7.056225643e+00 9.6e-04 0.01
9 1.3e-03 1.6e-03 3.4e-04 1.80e-01 7.747882511e+00 7.745219241e+00 3.3e-04 0.01
10 3.9e-04 4.8e-04 1.1e-04 6.10e-02 8.746640573e+00 8.755863362e+00 9.7e-05 0.02
11 1.6e-04 2.0e-04 4.1e-05 2.43e-01 9.156045415e+00 9.165462829e+00 4.1e-05 0.02
12 7.4e-05 9.2e-05 2.0e-05 1.16e-01 9.718738202e+00 9.731653358e+00 1.9e-05 0.02
13 2.0e-05 2.5e-05 5.1e-06 1.33e-01 1.052481442e+01 1.053893575e+01 5.1e-06 0.02
14 7.4e-06 9.2e-06 1.9e-06 1.00e-01 1.121615725e+01 1.123134021e+01 1.9e-06 0.02
15 2.6e-06 3.2e-06 7.1e-07 5.44e-02 1.217106043e+01 1.218933254e+01 6.5e-07 0.02
16 1.0e-06 1.3e-06 2.4e-07 2.51e-01 1.262960146e+01 1.264330114e+01 2.6e-07 0.02
17 4.2e-07 5.2e-07 1.0e-07 1.42e-01 1.334087744e+01 1.335537467e+01 1.0e-07 0.02
18 1.2e-07 1.5e-07 2.9e-08 1.48e-01 1.421315540e+01 1.422689355e+01 3.1e-08 0.03
19 3.7e-08 4.6e-08 8.2e-09 1.81e-01 1.500249764e+01 1.501487369e+01 9.3e-09 0.03
20 1.6e-08 2.0e-08 3.6e-09 8.93e-02 1.556087431e+01 1.557434873e+01 4.0e-09 0.03
21 7.1e-09 8.7e-09 1.4e-09 2.45e-01 1.568542825e+01 1.569571774e+01 1.8e-09 0.03
22 3.6e-09 4.4e-09 6.0e-10 4.15e-01 1.555160592e+01 1.555882397e+01 9.0e-10 0.03
23 1.6e-09 1.7e-09 1.5e-10 6.33e-01 1.542824640e+01 1.543152907e+01 3.3e-10 0.03
24 1.4e-09 8.8e-10 5.8e-11 9.82e-01 1.536661417e+01 1.536834079e+01 1.8e-10 0.03
25 5.4e-10 3.4e-10 1.5e-11 9.63e-01 1.533506942e+01 1.533580687e+01 6.8e-11 0.03
26 1.4e-10 8.6e-11 1.8e-12 1.06e+00 1.531902771e+01 1.531920600e+01 1.7e-11 0.04
27 4.5e-11 2.8e-11 3.5e-13 1.04e+00 1.531779320e+01 1.531785410e+01 5.7e-12 0.04
28 1.2e-11 7.5e-12 4.8e-14 1.02e+00 1.531706278e+01 1.531707888e+01 1.5e-12 0.04
29 1.2e-11 7.5e-12 4.8e-14 1.00e+00 1.531706278e+01 1.531707888e+01 1.5e-12 0.05
30 1.2e-11 7.5e-12 4.8e-14 1.14e+00 1.531706278e+01 1.531707888e+01 1.5e-12 0.06
Optimizer terminated. Time: 0.06
Interior-point solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: 1.5317062784e+01 nrm: 7e+08 Viol. con: 4e-03 var: 0e+00 barvar: 0e+00 cones: 6e-09
Dual. obj: 1.5317078882e+01 nrm: 1e+05 Viol. con: 0e+00 var: 6e-09 barvar: 5e-09 cones: 0e+00
Optimizer summary
Optimizer - time: 0.06
Interior-point - iterations : 31 time: 0.06
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: Solved
Optimal value (cvx_optval): +15.3171
ans =
1.1389
Calling Mosek 9.1.9: 355 variables, 173 equality constraints
For improved efficiency, Mosek is solving the dual problem.
MOSEK Version 9.1.9 (Build date: 2019-11-21 11:32:15)
Copyright © MOSEK ApS, Denmark. WWW: mosek.com
Platform: MACOSX/64-X86
MOSEK warning 710: #2 (nearly) zero elements are specified in sparse col ‘’ (3) of matrix ‘A’.
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 173
Cones : 12
Scalar variables : 67
Matrix variables : 8
Integer variables : 0
Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 0
Eliminator terminated.
Eliminator - tries : 1 time : 0.00
Lin. dep. - tries : 1 time : 0.00
Lin. dep. - number : 0
Presolve terminated. Time: 0.00
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 173
Cones : 12
Scalar variables : 67
Matrix variables : 8
Integer variables : 0
Optimizer - threads : 10
Optimizer - solved problem : the primal
Optimizer - Constraints : 159
Optimizer - Cones : 12
Optimizer - Scalar variables : 54 conic : 36
Optimizer - Semi-definite variables: 8 scalarized : 624
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 : 1.20e+04 after factor : 1.20e+04
Factor - dense dim. : 0 flops : 1.69e+06
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 4.0e+00 5.0e+00 7.9e+00 0.00e+00 6.885038836e+00 0.000000000e+00 1.0e+00 0.00
1 2.5e+00 3.0e+00 2.7e+00 1.64e+00 4.096348554e+00 9.059712311e-01 6.1e-01 0.00
2 9.4e-01 1.2e+00 4.9e-01 1.32e+00 3.063813667e+00 2.051876358e+00 2.3e-01 0.01
3 4.5e-01 5.6e-01 2.2e-01 8.25e-01 4.135971216e+00 3.529794308e+00 1.1e-01 0.01
4 1.5e-01 1.8e-01 4.8e-02 8.34e-01 4.221107232e+00 3.999197498e+00 3.7e-02 0.01
5 7.0e-02 8.7e-02 2.7e-02 3.65e-01 5.390299287e+00 5.219088032e+00 1.8e-02 0.01
6 2.7e-02 3.3e-02 7.6e-03 5.24e-01 5.625230276e+00 5.547446885e+00 6.7e-03 0.01
7 1.3e-02 1.6e-02 3.8e-03 2.57e-01 6.183249408e+00 6.131931759e+00 3.3e-03 0.01
8 3.2e-03 3.9e-03 8.6e-04 2.13e-01 7.143824719e+00 7.131523399e+00 7.9e-04 0.01
9 1.7e-03 2.1e-03 4.7e-04 1.06e-01 7.566681603e+00 7.561752159e+00 4.3e-04 0.01
10 5.9e-04 7.3e-04 1.6e-04 3.45e-02 8.374626685e+00 8.379756741e+00 1.5e-04 0.02
11 2.1e-04 2.6e-04 5.8e-05 5.11e-02 9.094160429e+00 9.105755260e+00 5.2e-05 0.02
12 6.1e-05 7.5e-05 1.5e-05 1.41e-01 9.739033956e+00 9.750508750e+00 1.5e-05 0.02
13 2.3e-05 2.9e-05 6.5e-06 1.37e-02 1.053714186e+01 1.055452581e+01 5.8e-06 0.02
14 6.9e-06 8.6e-06 1.8e-06 9.80e-02 1.136799911e+01 1.138435260e+01 1.7e-06 0.02
15 2.7e-06 3.4e-06 7.0e-07 1.27e-01 1.195399928e+01 1.197003293e+01 6.8e-07 0.02
16 1.1e-06 1.4e-06 2.9e-07 1.18e-01 1.264011553e+01 1.265625314e+01 2.8e-07 0.02
17 3.2e-07 4.0e-07 7.3e-08 1.96e-01 1.341787701e+01 1.343101541e+01 8.0e-08 0.02
18 8.8e-08 1.1e-07 2.5e-08 1.54e-02 1.468340229e+01 1.470351351e+01 2.2e-08 0.02
19 3.5e-08 4.3e-08 7.9e-09 3.50e-01 1.508754935e+01 1.510045660e+01 8.8e-09 0.03
20 2.1e-08 2.6e-08 5.1e-09 1.08e-01 1.548971441e+01 1.550474395e+01 5.2e-09 0.03
21 5.7e-09 7.0e-09 1.2e-09 1.84e-01 1.618738486e+01 1.619914071e+01 1.4e-09 0.03
22 2.0e-09 2.2e-09 3.7e-10 1.01e-01 1.664553417e+01 1.665675689e+01 4.4e-10 0.03
23 1.4e-09 6.1e-10 9.0e-11 2.12e-01 1.652405191e+01 1.653274544e+01 1.2e-10 0.03
24 9.6e-10 4.2e-10 8.1e-11 -3.98e-01 1.623076349e+01 1.624526898e+01 8.5e-11 0.03
25 4.8e-10 2.1e-10 5.7e-11 -5.94e-01 1.552785286e+01 1.555717925e+01 4.2e-11 0.03
26 1.6e-10 6.8e-11 3.1e-11 -7.90e-01 1.348724013e+01 1.356795217e+01 1.4e-11 0.04
27 5.3e-11 2.3e-11 1.8e-11 -9.50e-01 1.040862912e+01 1.063511014e+01 4.7e-12 0.04
28 1.2e-11 5.1e-12 8.1e-12 -9.85e-01 -4.454165743e+00 -3.451650378e+00 1.0e-12 0.04
29 2.1e-12 9.1e-13 3.4e-12 -9.95e-01 -8.984286375e+01 -8.441408941e+01 1.8e-13 0.05
30 4.8e-13 2.1e-13 1.6e-12 -1.00e+00 -3.791204711e+02 -3.560751588e+02 4.3e-14 0.05
31 1.3e-13 5.6e-14 8.3e-13 -1.00e+00 -1.460776609e+03 -1.374296668e+03 1.1e-14 0.05
32 3.7e-14 1.6e-14 4.4e-13 -1.00e+00 -4.448279883e+03 -4.150896345e+03 3.3e-15 0.06
33 2.8e-14 3.4e-15 2.1e-13 -1.00e+00 -2.213240599e+04 -2.073950066e+04 7.0e-16 0.06
34 1.8e-14 5.7e-16 8.6e-14 -1.00e+00 -1.223426174e+05 -1.138675940e+05 1.1e-16 0.06
35 1.6e-14 4.6e-16 8.0e-14 -1.00e+00 -1.515823824e+05 -1.411381340e+05 9.3e-17 0.06
36 1.4e-14 2.8e-16 6.5e-14 -1.00e+00 -2.487173739e+05 -2.317104976e+05 5.7e-17 0.07
37 1.4e-14 2.8e-16 6.5e-14 -1.00e+00 -2.487173739e+05 -2.317104976e+05 5.7e-17 0.07
38 1.4e-14 2.8e-16 6.5e-14 -1.00e+00 -2.487173739e+05 -2.317104976e+05 5.7e-17 0.08
Optimizer terminated. Time: 0.08
Interior-point solution summary
Problem status : ILL_POSED
Solution status : DUAL_ILLPOSED_CER
Primal. obj: -1.4092321280e-05 nrm: 3e+05 Viol. con: 6e-10 var: 0e+00 barvar: 0e+00 cones: 0e+00
Optimizer summary
Optimizer - time: 0.08
Interior-point - iterations : 39 time: 0.08
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: Failed
Optimal value (cvx_optval): NaN
My code is as follows.
cvx_begin sdp
cvx_solver mosek
cvx_quiet false;
variable W(N,N,K) hermitian semidefinite
variable apha(K)
variable deta(K)
variable beita(K)
variable kf(K)
variable fai(K)
variable gama(K)
variable kesai
expression X
RP1 = 0;
RP2 = 0;
KP = 0;
for r = 1:R
RP2=N_0*norm(Theta(:,:,r))^2 + RP2;
for k = 1:K
RP1=trace(W(:,:,k)*(Theta(:,:,r)*H_BR(:,:,r))'*(Theta(:,:,r)*H_BR(:,:,r)))+RP1;
KP =trace(W(:,:,k))+KP;
end
end
X=real(kesai-ratio*(RP1+KP/R+RP2));
maximize kesai
subject to
for k = 1:K
RI = 0;
RE = 0;
for r = 1:R
RI=N_0*norm(H_RI(:,k,r)'*Theta(:,:,r))^2+RI;
RE=N_0*norm(H_RE(:,:,r)'*Theta(:,:,r))^2+RE;
end
trace(W(:,:,k)*H_B_I(k,:)'*H_B_I(k,:))>=pow_p(kf(k),2); %1
trace(W(:,:,k)*H_B_E(:,:)'*H_B_E(:,:))<=yita4(k)^2+2*yita4(k)*(gama(k)-yita4(k));%4
apha_de = 0;
beita_de = 0;
for j = 1 : K
apha_de = trace(W(:,:,j) * H_B_I(k,:)' * H_B_I(k,:)) + apha_de;
beita_de = trace(W(:,:,j) * H_B_E(:,:)' * H_B_E(:,:)) + beita_de;
end
apha_de-trace(W(:,:,k)*H_B_I(k,:)'*H_B_I(k,:))+RI+N_0<=fai(k) ; %2
2*(yita2(k)/yita3(k))*kf(k)-(yita2(k)/yita3(k))^2*fai(k)>=apha(k); %3
[beita(k),gama(k);gama(k),beita_de-trace(W(:,:,k)*H_B_E(:,:)'*H_B_E(:,:))+RE+N_0]>=0; %5
trace(W(:,:,k))<=(PBS-WBS)/xi; %8
W(:,:,k)>=0; %10
deta(k)>=log(1+yita1(k))/log(2)+(beita(k)-yita1(k))./(log(2)*(1+yita1(k)));%7
log(apha(k))/log(2)-deta(k)>=kesai; %6
end
for r = 1:R
RS = N_0*norm(Theta(:,:,r))^2;
UR_C = 0;
for k =1:K
UR_C=trace(W(:,:,k)*(Theta(:,:,r)*H_BR(:,:,r))'*(Theta(:,:,r)*H_BR(:,:,r)))+UR_C;
end
zeta*(UR_C+RS)+M*WRIS <= PRIS; % 9
end
cvx_end
My code can iterate several times, but NAN will appear after several iterations. What is the reason for this. Help!