I need everyone’s help, thank you very much.
In a for loop, satisfying the condition is to output the optimal solution, but during the iteration process, the error Problem status: ILL will occur while running_ POSED
Solution status : DUAL_ ILLPOSED_ CER
How to solve it?
Mosek warning has a large number of null values, does this refer to the null value of a variable。
First iteration value
tau_max_t =
0.3036
0.3788
0.2991
0.0131
gammaa_t =
1.0403 1.0852
1.0177 0.1224
1.0006 0.4026
0.9999 0.0992
MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col '' (0) of matrix 'A'.
MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col '' (1) of matrix 'A'.
MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col '' (2) of matrix 'A'.
MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col '' (3) of matrix 'A'.
MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col '' (4) of matrix 'A'.
MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col '' (5) of matrix 'A'.
MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col '' (6) of matrix 'A'.
MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col '' (7) of matrix 'A'.
MOSEK warning 710: #10 (nearly) zero elements are specified in sparse col '' (8) of matrix 'A'.
MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col '' (9) of matrix 'A'.
Warning number 710 is disabled.
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 187
Cones : 10
Scalar variables : 179
Matrix variables : 17
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 started.
Freed constraints in eliminator : 0
Eliminator terminated.
Eliminator - tries : 2 time : 0.00
Lin. dep. - tries : 1 time : 0.01
Lin. dep. - number : 0
Presolve terminated. Time: 0.01
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 187
Cones : 10
Scalar variables : 179
Matrix variables : 17
Integer variables : 0
Optimizer - threads : 16
Optimizer - solved problem : the primal
Optimizer - Constraints : 177
Optimizer - Cones : 11
Optimizer - Scalar variables : 162 conic : 97
Optimizer - Semi-definite variables: 17 scalarized : 6356
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 : 1.29e+04
Factor - dense dim. : 0 flops : 7.75e+06
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 2.0e+01 2.2e+04 1.6e+06 0.00e+00 1.641198899e+06 -2.145220299e+00 1.0e+00 0.03
1 1.2e+01 1.3e+04 1.3e+06 -1.00e+00 1.641158579e+06 -4.167924771e+01 6.0e-01 0.09
2 3.2e+00 3.5e+03 6.6e+05 -1.00e+00 1.640832328e+06 -3.613791873e+02 1.6e-01 0.09
3 3.1e-01 3.4e+02 2.1e+05 -1.00e+00 1.636129109e+06 -4.900141851e+03 1.6e-02 0.09
4 5.6e-02 6.0e+01 8.6e+04 -9.99e-01 1.607235330e+06 -2.843630011e+04 2.8e-03 0.11
5 1.1e-02 1.2e+01 3.6e+04 -9.76e-01 1.364059422e+06 -1.343324849e+05 5.4e-04 0.11
6 4.2e-03 4.5e+00 1.6e+04 -6.13e-01 8.625567225e+05 -2.118976553e+05 2.1e-04 0.13
7 1.4e-03 1.5e+00 3.1e+03 2.11e-01 2.834847200e+05 -1.253587477e+05 7.1e-05 0.13
8 1.9e-04 2.0e-01 9.7e+01 1.01e+00 2.999168374e+04 -1.995532581e+04 9.3e-06 0.13
9 1.5e-05 1.6e-02 2.2e+00 1.05e+00 2.275501979e+03 -1.638963903e+03 7.5e-07 0.14
10 4.1e-06 4.5e-03 3.3e-01 1.01e+00 6.178094709e+02 -4.665877927e+02 2.1e-07 0.14
11 1.0e-06 1.1e-03 5.2e-02 1.00e+00 1.491658647e+02 -1.208836182e+02 5.2e-08 0.16
12 4.7e-07 5.1e-04 1.7e-02 1.00e+00 6.617900085e+01 -5.782218298e+01 2.4e-08 0.16
13 3.0e-07 3.2e-04 8.5e-03 9.97e-01 4.450190218e+01 -3.418554552e+01 1.5e-08 0.17
14 1.9e-07 2.1e-04 4.4e-03 9.89e-01 3.066487076e+01 -1.978790022e+01 9.6e-09 0.19
15 1.4e-07 1.5e-04 2.8e-03 9.70e-01 2.540322653e+01 -1.149529877e+01 6.9e-09 0.19
16 1.2e-07 1.3e-04 2.4e-03 9.49e-01 2.352450093e+01 -9.513169552e+00 6.2e-09 0.20
17 5.1e-08 5.5e-05 6.9e-04 9.30e-01 1.658489630e+01 2.121162864e+00 2.5e-09 0.20
18 3.7e-08 4.0e-05 4.6e-04 7.20e-01 1.548638457e+01 3.956670969e+00 1.8e-09 0.20
19 1.8e-08 1.9e-05 1.7e-04 6.93e-01 1.379420023e+01 7.576280608e+00 8.8e-10 0.22
20 8.4e-09 9.0e-06 5.9e-05 8.46e-01 1.269090293e+01 9.553951407e+00 4.2e-10 0.22
21 2.9e-09 3.2e-06 1.3e-05 8.96e-01 1.201500354e+01 1.085605166e+01 1.5e-10 0.23
22 1.7e-09 1.8e-06 6.3e-06 8.22e-01 1.187970626e+01 1.115773369e+01 8.4e-11 0.23
23 9.9e-10 1.1e-06 3.0e-06 8.49e-01 1.179030974e+01 1.134333448e+01 4.9e-11 0.25
24 5.8e-10 6.2e-07 1.5e-06 7.56e-01 1.175468411e+01 1.146335815e+01 2.9e-11 0.25
25 2.8e-10 3.0e-07 5.1e-07 8.35e-01 1.170487910e+01 1.155686186e+01 1.4e-11 0.25
26 1.3e-10 1.4e-07 1.9e-07 7.22e-01 1.169137387e+01 1.161070799e+01 6.5e-12 0.27
27 7.0e-11 7.5e-08 8.2e-08 7.88e-01 1.167964037e+01 1.163269914e+01 3.5e-12 0.27
28 2.9e-11 3.1e-08 2.6e-08 6.85e-01 1.167714395e+01 1.165437825e+01 1.4e-12 0.28
29 2.0e-11 2.2e-08 1.6e-08 6.97e-01 1.167660869e+01 1.165912591e+01 1.0e-12 0.28
30 6.5e-12 7.0e-09 3.9e-09 6.06e-01 1.167883106e+01 1.167168898e+01 3.2e-13 0.28
31 3.5e-12 3.8e-09 1.8e-09 6.29e-01 1.168036100e+01 1.167583393e+01 1.8e-13 0.30
32 1.6e-12 2.2e-09 7.3e-10 4.89e-01 1.168307827e+01 1.168034335e+01 8.1e-14 0.30
33 1.0e-12 2.3e-09 3.8e-10 6.11e-01 1.168363057e+01 1.168176972e+01 5.0e-14 0.31
34 3.0e-13 4.6e-09 8.8e-11 4.88e-01 1.168583398e+01 1.168507496e+01 1.5e-14 0.31
35 1.4e-13 2.3e-09 3.8e-11 4.84e-01 1.168678583e+01 1.168631675e+01 7.3e-15 0.33
36 4.8e-14 7.4e-10 8.9e-12 5.82e-01 1.168749627e+01 1.168730587e+01 2.4e-15 0.33
37 2.4e-14 3.7e-10 3.8e-12 5.37e-01 1.168790495e+01 1.168778806e+01 1.2e-15 0.34
38 1.2e-14 9.9e-10 1.5e-12 1.07e+00 1.168805471e+01 1.168799398e+01 6.9e-16 0.36
39 5.2e-15 1.8e-10 4.2e-13 1.01e+00 1.168811532e+01 1.168808964e+01 3.0e-16 0.36
40 5.1e-15 2.4e-10 3.8e-13 1.01e+00 1.168808104e+01 1.168805711e+01 2.8e-16 0.36
41 5.2e-15 3.2e-09 3.8e-13 1.23e+00 1.168780747e+01 1.168778363e+01 2.8e-16 0.38
42 2.7e-15 1.7e-09 2.8e-13 -9.99e-01 1.168771196e+01 1.168768889e+01 1.6e-16 0.38
43 2.7e-15 1.7e-09 2.8e-13 -9.98e-01 1.168771196e+01 1.168768889e+01 1.6e-16 0.39
44 2.7e-15 1.7e-09 2.8e-13 -9.93e-01 1.168771196e+01 1.168768889e+01 1.6e-16 0.41
Optimizer terminated. Time: 0.44
Interior-point solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: 1.1687711965e+01 nrm: 2e+07 Viol. con: 4e-10 var: 1e-11 barvar: 0e+00 cones: 0e+00
Dual. obj: 1.1687688884e+01 nrm: 1e+06 Viol. con: 0e+00 var: 3e-06 barvar: 3e-07 cones: 0e+00
Optimizer summary
Optimizer - time: 0.44
Interior-point - iterations : 45 time: 0.42
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): +3.04764
ans =
3.0586
rho =
0.0011
Second iteration value
u_t =
0.6432 - 0.7657i
0.6432 - 0.7657i
0.6434 - 0.7655i
0.6436 - 0.7654i
0.6431 - 0.7658i
0.9927 - 0.1205i
0.8736 + 0.4867i
0.9866 - 0.1631i
0.9968 + 0.0804i
0.6923 - 0.7216i
tau_max_t =
0.1323
0.1849
0.1468
0.0078
gammaa_t =
1.0076 1.1202
1.0440 0.8631
1.0030 0.8569
0.9988 0.8344
Saving prefs...done.
Calling Mosek 9.1.9: 3243 variables, 187 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 (c) MOSEK ApS, Denmark. WWW: mosek.com
Platform: Windows/64-X86
MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col '' (0) of matrix 'A'.
MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col '' (1) of matrix 'A'.
MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col '' (2) of matrix 'A'.
MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col '' (3) of matrix 'A'.
MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col '' (4) of matrix 'A'.
MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col '' (5) of matrix 'A'.
MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col '' (6) of matrix 'A'.
MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col '' (7) of matrix 'A'.
MOSEK warning 710: #10 (nearly) zero elements are specified in sparse col '' (8) of matrix 'A'.
MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col '' (9) of matrix 'A'.
Warning number 710 is disabled.
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 187
Cones : 10
Scalar variables : 179
Matrix variables : 17
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 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 : 187
Cones : 10
Scalar variables : 179
Matrix variables : 17
Integer variables : 0
Optimizer - threads : 16
Optimizer - solved problem : the primal
Optimizer - Constraints : 177
Optimizer - Cones : 11
Optimizer - Scalar variables : 162 conic : 97
Optimizer - Semi-definite variables: 17 scalarized : 6356
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 : 1.29e+04
Factor - dense dim. : 0 flops : 7.75e+06
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 2.0e+01 2.2e+04 1.6e+06 0.00e+00 1.641198899e+06 -2.154131558e+00 1.0e+00 0.03
1 9.7e+00 1.0e+04 1.1e+06 -1.00e+00 1.641162170e+06 -3.765691394e+01 4.8e-01 0.09
2 3.2e+00 3.4e+03 6.5e+05 -1.00e+00 1.640905651e+06 -2.876870081e+02 1.6e-01 0.09
3 8.3e-02 9.0e+01 1.1e+05 -1.00e+00 1.628429594e+06 -1.213092799e+04 4.2e-03 0.11
4 1.4e-02 1.5e+01 4.2e+04 -9.92e-01 1.502572518e+06 -7.086230096e+04 6.8e-04 0.11
5 5.9e-03 6.4e+00 2.3e+04 -7.49e-01 1.153117180e+06 -1.243531654e+05 2.9e-04 0.11
6 2.0e-03 2.2e+00 6.5e+03 -2.53e-01 5.002638183e+05 -1.430414010e+05 1.0e-04 0.13
7 4.7e-04 5.1e-01 4.5e+02 9.00e-01 8.467091941e+04 -5.300020044e+04 2.4e-05 0.13
8 2.6e-05 2.8e-02 4.7e+00 1.16e+00 3.543301662e+03 -3.364172961e+03 1.3e-06 0.14
9 4.4e-06 4.8e-03 3.5e-01 1.01e+00 5.923657726e+02 -5.660902339e+02 2.2e-07 0.14
10 1.5e-06 1.6e-03 8.3e-02 1.00e+00 2.058705809e+02 -1.848101223e+02 7.4e-08 0.14
11 5.4e-07 5.9e-04 1.9e-02 1.00e+00 7.104908624e+01 -7.174131020e+01 2.7e-08 0.16
12 3.2e-07 3.5e-04 8.9e-03 9.96e-01 4.405730703e+01 -4.047194529e+01 1.6e-08 0.16
13 2.1e-07 2.2e-04 4.7e-03 9.91e-01 2.948437213e+01 -2.482968297e+01 1.0e-08 0.17
14 1.5e-07 1.6e-04 2.9e-03 9.73e-01 2.440353045e+01 -1.454404797e+01 7.3e-09 0.19
15 9.1e-08 9.9e-05 1.5e-03 9.42e-01 1.973151096e+01 -5.404777804e+00 4.6e-09 0.19
16 7.5e-08 8.1e-05 1.2e-03 8.95e-01 1.802885335e+01 -3.096239031e+00 3.8e-09 0.20
17 3.4e-08 3.7e-05 4.1e-04 8.41e-01 1.474868791e+01 3.998411417e+00 1.7e-09 0.20
18 1.8e-08 1.9e-05 1.6e-04 6.42e-01 1.319782923e+01 7.113627459e+00 9.0e-10 0.22
19 6.7e-09 7.2e-06 3.9e-05 8.23e-01 1.207882313e+01 9.673291245e+00 3.3e-10 0.22
20 1.8e-09 2.0e-06 6.4e-06 9.24e-01 1.158827113e+01 1.088635571e+01 9.2e-11 0.22
21 1.0e-09 1.1e-06 2.8e-06 8.51e-01 1.148382221e+01 1.107558569e+01 5.0e-11 0.23
22 5.8e-10 6.2e-07 1.3e-06 8.55e-01 1.142689004e+01 1.117718928e+01 2.9e-11 0.23
23 4.0e-10 4.4e-07 8.0e-07 7.47e-01 1.141404918e+01 1.122397185e+01 2.0e-11 0.25
24 1.8e-10 1.9e-07 2.5e-07 8.63e-01 1.137525420e+01 1.128587053e+01 9.0e-12 0.25
25 7.6e-11 8.1e-08 8.1e-08 7.49e-01 1.136505480e+01 1.132145064e+01 3.8e-12 0.25
26 3.3e-11 3.6e-08 2.6e-08 7.88e-01 1.135862762e+01 1.133742068e+01 1.7e-12 0.27
27 1.8e-11 1.9e-08 1.2e-08 6.50e-01 1.135879706e+01 1.134540164e+01 8.9e-13 0.27
28 1.0e-11 1.1e-08 5.7e-09 7.67e-01 1.135742542e+01 1.134900303e+01 5.2e-13 0.28
29 3.4e-12 3.6e-09 1.4e-09 6.35e-01 1.135835707e+01 1.135490650e+01 1.7e-13 0.28
30 1.7e-12 1.9e-09 6.3e-10 5.27e-01 1.135969748e+01 1.135743256e+01 8.7e-14 0.28
31 9.2e-13 9.9e-10 2.7e-10 6.90e-01 1.136004559e+01 1.135869911e+01 4.6e-14 0.30
32 3.4e-13 8.2e-10 8.2e-11 5.21e-01 1.136117867e+01 1.136051401e+01 1.7e-14 0.30
33 2.2e-13 1.0e-09 5.0e-11 4.80e-01 1.136149887e+01 1.136098794e+01 1.1e-14 0.31
34 6.7e-14 1.6e-09 1.2e-11 4.48e-01 1.136228986e+01 1.136207863e+01 3.4e-15 0.31
35 3.4e-14 2.5e-09 5.2e-12 5.09e-01 1.136258214e+01 1.136244933e+01 1.7e-15 0.31
36 1.3e-14 9.2e-10 1.5e-12 5.77e-01 1.136280147e+01 1.136273990e+01 6.4e-16 0.33
37 7.6e-15 3.6e-09 9.1e-13 1.38e+00 1.136310026e+01 1.136305718e+01 4.8e-16 0.33
38 4.3e-15 1.8e-09 3.7e-13 7.45e-01 1.136301246e+01 1.136298793e+01 2.4e-16 0.34
39 4.9e-15 9.2e-10 3.6e-13 1.35e+00 1.136290011e+01 1.136287657e+01 2.4e-16 0.34
40 3.0e-15 6.9e-10 4.2e-13 -9.17e-01 1.136282318e+01 1.136278973e+01 2.0e-16 0.36
41 1.8e-15 4.0e-10 3.2e-13 -5.17e-01 1.136224825e+01 1.136221574e+01 1.3e-16 0.38
42 5.3e-15 7.3e-10 1.8e-13 -7.10e-01 1.135976732e+01 1.135974529e+01 5.3e-17 0.38
43 1.4e-15 2.6e-10 8.9e-14 -9.03e-01 1.134619522e+01 1.134620968e+01 1.5e-17 0.39
44 5.6e-16 1.1e-10 5.8e-14 -9.81e-01 1.132164590e+01 1.132171903e+01 6.5e-18 0.39
45 1.1e-16 2.7e-11 2.8e-14 -9.95e-01 1.117337256e+01 1.117377200e+01 1.5e-18 0.39
46 9.0e-17 2.2e-11 2.5e-14 -9.96e-01 1.112625385e+01 1.112675747e+01 1.2e-18 0.41
47 8.9e-17 2.2e-11 2.4e-14 -8.42e-01 1.114727884e+01 1.114776239e+01 1.2e-18 0.41
48 8.9e-17 2.2e-11 2.4e-14 -8.07e-01 1.114727884e+01 1.114776239e+01 1.2e-18 0.42
49 8.9e-17 2.2e-11 2.4e-14 -8.06e-01 1.114727884e+01 1.114776239e+01 1.2e-18 0.44
Optimizer terminated. Time: 0.47
Interior-point solution summary
Problem status : ILL_POSED
Solution status : DUAL_ILLPOSED_CER
Primal. obj: 4.5261768468e-07 nrm: 3e+02 Viol. con: 6e-07 var: 5e-19 barvar: 0e+00 cones: 3e-08
Optimizer summary
Optimizer - time: 0.47
Interior-point - iterations : 50 time: 0.45
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
for e_i=1:100
cvx_begin
cvx_solver mosek
cvx_save_prefs
variable U(N_all+1,N_all+1) hermitian
variable uu(N_all+1) complex
variables relax_IN_VB(K,L) relax_IN_Vr(K,L) relax_S_B(K,L) relax_S_R(K,L) rho tau_max(K) gammaa(K,L)
expressions A(M+N_all,M+N_all,K) a0(M+N_all,M+N_all,K,L) b0(M+N_all,K,L) c0(K,L) LMI_S(M+N_all+1,M+N_all+1,K,L) ...
right_up(K,L) e(K,L) delta(K,L) LMI_IN(M+N_all+2,M+N_all+2,K,L) RR_lp(K) S2(K) LIM(N_all+2,N_all+2) ;
a=zeros(N_all,N_all);
ut=[u_t;1];
for l=1:L
E(l,:)=[H_rE(:,l)',h_BE(:,l)'];
for k=1:K
w_temp=zeros(M,M);
for j=k+1:K
w_temp=w_temp+w(:,j)*w(:,j)';
end
[UU,SS,VV]=svd(G*w_temp*G');
for n=1:N_all
ss(:,:,n)=[diag((SS(n,n)*UU(:,n))),zeros(N_all,1)];
vv(:,:,n)=[diag(VV(:,n)');zeros(1,N_all)];
a=a+ss(:,:,n)*U*vv(:,:,n);
end
A(:,:,k)=[a, diag(uu(1:N_all)')*G* w_temp;...
w_temp*G'*diag(uu(1:N_all)), w_temp];
a0(:,:,k,l)=A(:,:,k)+relax_S_B(k,l)*[zeros(N_all,N_all),zeros(N_all,M);zeros(M,N_all),eye(M)]...
+relax_S_R(k,l)*[eye(N_all),zeros(N_all,M);zeros(M,N_all),zeros(M,M)];
b0(:,k,l)=A(:,:,k)'*E(1,:)';
c0(k,l)=E(1,:)*A(:,:,k)*E(1,:)'+noise-gammaa(k,l)-relax_S_R(k,l)*epsilong_R(l)-relax_S_B(k,l)*epsilong_B(l);
LMI_S(:,:,k,l)=[a0(:,:,k,l) b0(:,k,l);...
b0(:,k,l)' c0(k,l)];
right_up(k,l)=(2^(tau_max_t(k)))*gammaa(k,l)+(2^(tau_max_t(k)))*gammaa_t(k,l)*log(2)...
*(tau_max(k)-tau_max_t(k))-gammaa(k,l);
e(k,l)=right_up(k,l)-relax_IN_VB(k,l)-relax_IN_Vr(k,l)*N_all;
delta(k,l)=(uu(1:N_all)'*diag(H_rE(:,l)')*G+h_BE(:,l)')*w(:,k);
LMI_IN(:,:,k,l)=[e(k,l) delta(k,l) zeros(1,M) zeros(1,N_all);...
delta(k,l)' 1-relax_IN_VB(k,l) h_BE_error(l)*w(:,k)' h_rE_error(l)*w(:,k)'*G';...
zeros(M,1) h_BE_error(l)*w(:,k) relax_IN_VB(k,l)*eye(M) zeros(M,N_all);...
zeros(N_all,1) h_rE_error(l)*G*w(:,k) zeros(N_all,M) relax_IN_Vr(k,l)*eye(N_all)];
end
end
LMI=[1,uu';uu,U];
for k=1:K
w_temp1=0;w_temp2=0;
for i=k+1:K
w_temp1=w_temp1+pow_abs((u_t'*H(:,:,k)+h_Bk(:,k)')*w(:,i),2);
w_temp2=w_temp2+pow_abs((uu(1:N_all)'*H(:,:,k)+h_Bk(:,k)')*w(:,i),2);
end
w_temp3=pow_abs((u_t'*H(:,:,k)+h_Bk(:,k)')*w(:,k),2);
w_temp4=pow_abs((uu(1:N_all)'*H(:,:,k)+h_Bk(:,k)')*w(:,k),2);
RR_lp(k)=log(1+(w_temp3)/(w_temp1+noise))/log(2)+2*real((u_t'*H(:,:,k)+h_Bk(:,k)')*w(:,k)*...
((uu(1:N_all)'*H(:,:,k)+h_Bk(:,k)')*w(:,k)))/((w_temp1+noise)*log(2))...
-(w_temp3)*(w_temp2+noise+w_temp4)/((w_temp1+noise)*((w_temp1+noise)+w_temp3)*log(2))-w_temp3/((w_temp1+noise)*log(2));
S2(k)=RR_lp(k)-tau_max(k);
end
maximize sum(S2)-f*rho
subject to
diag(U)==1;
for n=1:N_all+1
2*real(ut(n)*uu(n)')-abs(ut(n))^2>=1-rho;%正惩罚项
end
for k=2:K
for j=1:k-1
for n=j+1:K
real(trace(P(:,:,k)*w(:,j)*w(:,j)'*P(:,:,k)'*U))>=real(trace(P(:,:,k)*w(:,n)*w(:,n)'*P(:,:,k)'*U));
end
end
end
LMI==hermitian_semidefinite(N_all+2);
for l=1:L
for k=1:K
LMI_S(:,:,k,l) ==hermitian_semidefinite(M+N_all+1);
LMI_IN(:,:,k,l) ==hermitian_semidefinite(M+N_all+2);
relax_IN_VB(k,l)>0;
relax_IN_Vr(k,l)>0;
relax_S_B(k,l)>0;
relax_S_R(k,l)>0;
gammaa(k,l)>0;
RR_lp(k)-tau_max(k)>0;
end
end
cvx_end
sum(S2)
rho
if cvx_status(1)=='S' || cvx_status(3)=='a'
S(e_i+1)=sum(S2);
u_t=uu(1:N_all)
tau_max_t=tau_max
gammaa_t=gammaa
if rho<0.001&&abs(S(e_i+1)-S(e_i))/S(e_i+1)<0.001
break;
end
else
break
end
end
I think the iteration value is relatively normal and has not become particularly large or small, but I don’t know why the next loop failed.