How to deal trace(X^H*A*X) in cvx

It seems the value of square_pos(norm(…,‘fro’)) is -1 or 1.
image

image

Please show a complete reproducible example, starting from a fresh MATLAB session. Copy and paste your code into a post.

If square_pos of anything comes out to -1, or any norm of anything is negative, something is wrong. You are probably messing something up.

clc 
clear all
M=20;
Nt=5;
Nr=4;
Ne=4;
sigma_s=10^(-9);
sigma_e=sigma_s;
sigma_p=sigma_s;
theta=0.7;
epxier=0.8;
Pt=1;
kama_p=3;
EH0=10^(-7);
d0=3;
H_SI=sqrt(0.5)*(randn(M,Nt)+1j*randn(M,Nt)); %--
H_SS=sqrt(0.5)*(randn(Nr,Nt)+1j*randn(Nr,Nt));% --
H_SE=sqrt(0.5)*(randn(Ne,Nt)+1j*randn(Ne,Nt)); %--
h_SP=sqrt(0.5)*(randn(1,Nt)+1j*randn(1,Nt));% ---
h_PI=sqrt(0.5)*(randn(M,1)+1j*randn(M,1)); %---
h_PS=sqrt(0.5)*(randn(Nr,1)+1j*randn(Nr,1)); %--
h_PE=sqrt(0.5)*(randn(Ne,1)+1j*randn(Ne,1));% --  
h_PP=sqrt(0.5)*(randn(1,1)+1j*randn(1,1));%---
H_IE=sqrt(0.5)*(randn(Ne,M)+1j*randn(Ne,M));% ---
H_IS=sqrt(0.5)*(randn(Nr,M)+1j*randn(Nr,M));%---
dx=2.5;
dy=10;
dps=5;
r_SS=8;
r_SE=8;
r_SP=sqrt(dx^2+dps^2);
r_SI=sqrt(dx^2+dy^2);
r_IS=sqrt((dy-r_SS)^2+dx^2);
r_IE=sqrt((dy-r_SE)^2+dx^2);
r_PP=dx;
r_PS=dps+r_SS;
r_PE=dps+r_SE;
r_PI=sqrt(dx^2+(dy+dps)^2);
L0=0.01;
H_SI=H_SI*sqrt(L0*((r_SI)^-2.2));%-
H_SS=H_SS*sqrt(L0*((r_SS)^-2.7));%-
H_SE=H_SE*sqrt(L0*((r_SE)^-2.7));%-
h_SP=h_SP*sqrt(L0*((r_SP)^-2.7));%-
h_PI=h_PI*sqrt(L0*((r_PI)^-2.2));%-
h_PS=h_PS*sqrt(L0*((r_PS)^-2.7));%
h_PE=h_PE*sqrt(L0*((r_PE)^-2.7));%
h_PP=h_PP*sqrt(L0*((r_PP)^-2.7));%-
H_IE=H_IE*sqrt(L0*((r_IE)^-2.2));%-
H_IS=H_IS*sqrt(L0*((r_IS)^-2.2));%-
H_SP=h_SP'*h_SP;   
q0=exp(j*2*pi*randn(M,1));
G0=diag(q0);   
V0=sqrt(1/(Nt*d0))*exp(j*2*pi*randn(Nt,d0));
H1=H_SS+H_IS*G0*H_SI;
H2=H_SE+H_IE*G0*H_SI;        
U1=inv(((h_PS+H_IS*G0*h_PI)*(h_PS+H_IS*G0*h_PI)'*Pt+sigma_s*eye(Nr)+H1*V0*V0'*H1'))*H1*V0;        
E1=(eye(d0)-U1'*H1*V0)*(eye(d0)-U1'*H1*V0)'+U1'*((h_PS+H_IS*G0*h_PI)*(h_PS+H_IS*G0*h_PI)'*Pt+sigma_s*eye(Nr))*U1;
W1=inv(E1);
W3=inv((h_PE+H_IE*G0*h_PI)*(h_PE+H_IE*G0*h_PI)'*Pt+eye(Ne)*sigma_e+H2*V0*V0'*H2');
t0=real(trace(V0'*H1'*U1*W1*U1'*H1*V0)-trace(W1*V0'*H1'*U1)-trace(W1*U1'*H1*V0)+trace(V0'*H2'*W3*H2*V0));
while 1   %%%Solve V
    cvx_begin quiet
    cvx_solver mosek 
    variable V(Nt,d0)
    minimize (square_pos(norm(sqrtm(W1)*(U1'*H1*V),'fro'))+square_pos(norm(sqrtm(W3)*(H2*V),'fro'))-real(trace(W1*V'*H1'*U1))-real(trace(W1*U1'*H1*V)))
    subject to
        square_pos(norm(V,2))<=1;
        square_pos(norm(sqrtm(H_SP)*V,2))<=Pt*abs(h_PP)^2/kama_p-sigma_p;
        2*real(trace(V'*H2'*H2*V0))>=EH0/(epxier*(1-theta))-(square_pos(norm(h_PE+H_IE*G0*h_PI,2))*Pt+sigma_e)+real(trace(V0'*H2'*H2*V0));
    cvx_end
    t1=real(trace(V'*H1'*U1*W1*U1'*H1*V)-trace(W1*V'*H1'*U1)-trace(W1*U1'*H1*V)+trace(V'*H2'*W3*H2*V));
    t11=(square_pos(norm(sqrtm(W1)*(U1'*H1*V),'fro'))+square_pos(norm(sqrtm(W3)*(H2*V),'fro'))-real(trace(W1*V'*H1'*U1))-real(trace(W1*U1'*H1*V)));    
    t1=trace(V'*H1'*U1*W1*U1'*H1*V)
    t2=square_pos(norm(sqrtm(W1)*(U1'*H1*V),'fro'))    
    t=(t0-t1)/t0;
    if(abs(t)<10^-2)
        break
    end
    V0=V;
    t0=t1;    
end

I removed the quiet option, so that the solver and CVX output is shown. Everything looks fine. Not at all like whatever it was you showed.

Calling Mosek 9.2.20: 167 variables, 31 equality constraints
For improved efficiency, Mosek is solving the dual problem.

MOSEK Version 9.2.21 (Build date: 2020-9-1 11:11:27)
Copyright © MOSEK ApS, Denmark. WWW: mosek.com
Platform: Windows/64-X86

Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 31
Cones : 6
Scalar variables : 67
Matrix variables : 2
Integer variables : 0

Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 2
Eliminator terminated.
Eliminator - tries : 1 time : 0.00
Lin. dep. - tries : 1 time : 0.00
Lin. dep. - number : 0
Presolve terminated. Time: 0.05
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 31
Cones : 6
Scalar variables : 67
Matrix variables : 2
Integer variables : 0

Optimizer - threads : 8
Optimizer - solved problem : the primal
Optimizer - Constraints : 19
Optimizer - Cones : 6
Optimizer - Scalar variables : 57 conic : 56
Optimizer - Semi-definite variables: 2 scalarized : 172
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 : 184 after factor : 190
Factor - dense dim. : 0 flops : 6.47e+04
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 3.0e+02 6.6e+01 7.0e+00 0.00e+00 5.000421364e+00 -1.000000000e+00 1.0e+00 0.08
1 1.4e+02 3.1e+01 4.8e+00 -1.00e+00 -1.844947876e+01 -2.328952457e+01 4.6e-01 0.22
2 3.1e+01 6.9e+00 2.3e+00 -1.00e+00 -8.173476644e+01 -7.910941386e+01 1.0e-01 0.22
3 6.9e+00 1.5e+00 1.1e+00 -1.00e+00 -1.558770785e+01 2.169598180e+01 2.3e-02 0.23
4 1.6e+00 3.6e-01 5.2e-01 -1.00e+00 1.295306038e+03 1.471660036e+03 5.5e-03 0.23
5 4.7e-01 1.0e-01 2.6e-01 -9.69e-01 6.941121688e+03 7.530801279e+03 1.5e-03 0.25
6 2.1e-01 4.6e-02 1.6e-01 -8.26e-01 1.592851972e+04 1.695003517e+04 7.0e-04 0.27
7 1.1e-01 2.5e-02 1.1e-01 -7.48e-01 2.865868558e+04 3.039795088e+04 3.7e-04 0.27
8 6.6e-02 1.4e-02 4.7e-02 -1.84e-01 4.094442197e+04 4.189788013e+04 2.2e-04 0.28
9 2.7e-02 5.9e-03 2.7e-02 -4.05e-01 6.644786733e+04 6.829513244e+04 8.9e-05 0.28
10 1.1e-02 2.4e-03 6.2e-03 6.30e-01 8.433128292e+04 8.491538249e+04 3.6e-05 0.28
11 6.4e-03 1.4e-03 3.1e-03 6.98e-01 8.954098631e+04 8.999380411e+04 2.1e-05 0.30
12 2.0e-03 4.4e-04 5.5e-04 9.71e-01 9.732338038e+04 9.746639681e+04 6.6e-06 0.30
13 1.0e-03 2.3e-04 2.5e-04 8.83e-01 9.841501124e+04 9.852323822e+04 3.5e-06 0.31
14 2.4e-04 5.4e-05 2.6e-05 1.16e+00 1.000163434e+05 1.000369433e+05 8.1e-07 0.31
15 9.8e-05 2.1e-05 7.6e-06 9.56e-01 1.001887509e+05 1.001998658e+05 3.2e-07 0.33
16 1.4e-05 3.2e-06 3.2e-07 1.21e+00 1.003288108e+05 1.003297199e+05 4.8e-08 0.33
17 2.8e-06 6.1e-07 2.5e-08 1.13e+00 1.003405834e+05 1.003407263e+05 9.3e-09 0.34
18 4.6e-09 1.6e-07 1.1e-10 1.00e+00 1.003430997e+05 1.003431001e+05 1.5e-10 0.34
19 4.4e-09 1.6e-07 9.1e-11 1.00e+00 1.003430962e+05 1.003430966e+05 1.5e-10 0.36
20 3.3e-09 1.2e-07 5.0e-11 1.00e+00 1.003430690e+05 1.003430692e+05 1.1e-10 0.36
21 2.9e-09 1.0e-07 4.4e-11 1.00e+00 1.003430588e+05 1.003430590e+05 9.8e-11 0.38
22 2.9e-09 1.0e-07 3.7e-11 1.00e+00 1.003430577e+05 1.003430579e+05 9.6e-11 0.39
23 2.7e-09 9.4e-08 3.3e-11 1.00e+00 1.003430533e+05 1.003430535e+05 9.0e-11 0.39
24 1.4e-09 6.0e-08 1.1e-11 1.00e+00 1.003430205e+05 1.003430206e+05 4.6e-11 0.39
25 1.3e-09 6.3e-08 5.9e-12 1.00e+00 1.003430195e+05 1.003430196e+05 4.4e-11 0.41
26 1.2e-09 6.6e-08 2.2e-12 1.00e+00 1.003430175e+05 1.003430176e+05 4.1e-11 0.42
27 1.2e-09 6.6e-08 2.2e-12 1.00e+00 1.003430175e+05 1.003430176e+05 4.1e-11 0.42
28 1.2e-09 6.8e-08 7.5e-12 1.00e+00 1.003430156e+05 1.003430157e+05 3.9e-11 0.44
29 1.1e-09 7.0e-08 4.0e-12 1.00e+00 1.003430152e+05 1.003430152e+05 3.8e-11 0.44
30 1.1e-09 7.8e-08 8.1e-12 1.00e+00 1.003430134e+05 1.003430135e+05 3.6e-11 0.45
31 1.1e-09 7.5e-08 4.3e-12 1.00e+00 1.003430132e+05 1.003430133e+05 3.6e-11 0.45
32 9.9e-10 7.8e-08 1.6e-12 1.00e+00 1.003430116e+05 1.003430117e+05 3.3e-11 0.45
33 9.9e-10 7.8e-08 1.6e-12 1.00e+00 1.003430116e+05 1.003430117e+05 3.3e-11 0.47
34 9.9e-10 7.9e-08 5.1e-12 1.00e+00 1.003430116e+05 1.003430117e+05 3.3e-11 0.47
35 5.0e-10 1.3e-07 3.4e-12 1.00e+00 1.003429995e+05 1.003429995e+05 1.7e-11 0.48
Optimizer terminated. Time: 0.56

Interior-point solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: 1.0034299948e+05 nrm: 2e+05 Viol. con: 1e-03 var: 0e+00 barvar: 0e+00 cones: 0e+00
Dual. obj: 1.0034299952e+05 nrm: 1e+05 Viol. con: 0e+00 var: 9e-10 barvar: 2e-09 cones: 4e-14
Optimizer summary
Optimizer - time: 0.56
Interior-point - iterations : 35 time: 0.48
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): -100343

t1 =
9.169133569916600e+04 + 4.652019924833439e-08i
t2 =
9.169133569916851e+04

Calling Mosek 9.2.20: 167 variables, 31 equality constraints
For improved efficiency, Mosek is solving the dual problem.

MOSEK Version 9.2.21 (Build date: 2020-9-1 11:11:27)
Copyright © MOSEK ApS, Denmark. WWW: mosek.com
Platform: Windows/64-X86

Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 31
Cones : 6
Scalar variables : 67
Matrix variables : 2
Integer variables : 0

Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 2
Eliminator terminated.
Eliminator - tries : 1 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 : 31
Cones : 6
Scalar variables : 67
Matrix variables : 2
Integer variables : 0

Optimizer - threads : 8
Optimizer - solved problem : the primal
Optimizer - Constraints : 19
Optimizer - Cones : 6
Optimizer - Scalar variables : 57 conic : 56
Optimizer - Semi-definite variables: 2 scalarized : 172
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 : 184 after factor : 190
Factor - dense dim. : 0 flops : 6.47e+04
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 3.0e+02 8.9e+01 7.0e+00 0.00e+00 5.000421364e+00 -1.000000000e+00 1.0e+00 0.06
1 1.4e+02 4.1e+01 4.8e+00 -1.00e+00 -3.521003872e+01 -4.005120730e+01 4.6e-01 0.22
2 3.2e+01 9.3e+00 2.3e+00 -1.00e+00 -1.757025799e+02 -1.730886308e+02 1.0e-01 0.25
3 6.7e+00 2.0e+00 1.1e+00 -1.01e+00 -3.017449348e+02 -2.626666733e+02 2.2e-02 0.25
4 1.5e+00 4.5e-01 5.1e-01 -1.01e+00 8.368250793e+02 1.033324386e+03 5.1e-03 0.25
5 4.3e-01 1.3e-01 2.6e-01 -9.83e-01 6.885029031e+03 7.550701921e+03 1.4e-03 0.27
6 2.3e-01 6.9e-02 1.7e-01 -8.24e-01 1.391737450e+04 1.490777331e+04 7.7e-04 0.27
7 1.2e-01 3.5e-02 1.2e-01 -7.52e-01 2.760611168e+04 2.938128943e+04 4.0e-04 0.28
8 6.9e-02 2.0e-02 4.9e-02 -2.69e-01 4.033407789e+04 4.127126859e+04 2.3e-04 0.28
9 2.6e-02 7.6e-03 2.5e-02 -3.48e-01 6.821331993e+04 6.997707239e+04 8.6e-05 0.30
10 1.1e-02 3.2e-03 6.2e-03 6.88e-01 8.528679009e+04 8.588501652e+04 3.6e-05 0.30
11 6.4e-03 1.9e-03 3.3e-03 7.01e-01 8.968943913e+04 9.017419664e+04 2.1e-05 0.30
12 1.8e-03 5.4e-04 5.0e-04 9.78e-01 9.760694871e+04 9.774325038e+04 6.1e-06 0.31
13 8.8e-04 2.6e-04 2.0e-04 8.98e-01 9.874246113e+04 9.883730651e+04 2.9e-06 0.31
14 2.1e-04 6.3e-05 2.1e-05 1.16e+00 1.000578643e+05 1.000759994e+05 7.1e-07 0.33
15 8.7e-05 2.6e-05 6.4e-06 9.50e-01 1.002058632e+05 1.002157431e+05 2.9e-07 0.34
16 1.3e-05 4.0e-06 2.8e-07 1.23e+00 1.003295562e+05 1.003303774e+05 4.4e-08 0.34
17 1.8e-06 1.6e-06 1.4e-08 9.95e-01 1.003424898e+05 1.003426015e+05 6.6e-09 0.34
18 6.2e-09 8.7e-08 1.5e-10 1.00e+00 1.003430495e+05 1.003430499e+05 8.7e-11 0.36
19 5.8e-09 8.1e-08 6.9e-11 1.00e+00 1.003430456e+05 1.003430460e+05 8.2e-11 0.36
20 3.0e-09 8.4e-08 6.9e-12 1.00e+00 1.003430166e+05 1.003430168e+05 4.1e-11 0.38
21 2.9e-09 8.2e-08 1.1e-11 1.00e+00 1.003430165e+05 1.003430167e+05 4.1e-11 0.38
22 2.2e-09 1.2e-07 1.0e-11 1.00e+00 1.003430092e+05 1.003430094e+05 3.1e-11 0.39
23 2.2e-09 1.2e-07 1.0e-11 1.00e+00 1.003430092e+05 1.003430094e+05 3.1e-11 0.39
24 2.1e-09 1.2e-07 5.9e-12 1.00e+00 1.003430085e+05 1.003430087e+05 3.0e-11 0.41
25 1.6e-09 1.6e-07 7.5e-12 1.00e+00 1.003430032e+05 1.003430033e+05 2.2e-11 0.41
26 8.1e-10 2.5e-07 3.0e-12 1.00e+00 1.003429952e+05 1.003429953e+05 1.1e-11 0.42
Optimizer terminated. Time: 0.48

Interior-point solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: 1.0034299520e+05 nrm: 2e+05 Viol. con: 2e-03 var: 0e+00 barvar: 0e+00 cones: 0e+00
Dual. obj: 1.0034299525e+05 nrm: 1e+05 Viol. con: 0e+00 var: 1e-09 barvar: 3e-09 cones: 0e+00
Optimizer summary
Optimizer - time: 0.48
Interior-point - iterations : 26 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): -100343

t1 =
9.169128964726381e+04 + 4.651565177482553e-08i
t2 =
9.169128964726634e+04

I removed the quiet option, there still with t2=-1, something wrong with my matlab or cvx?

Show your code and the results all at once. I have no idea what is going on when you show two different windows, and perhaps, neither do you.

Too strange,dont konw how to deal next step.

Following is the cvx output messeage:

Calling Mosek 8.0.0.60: 167 variables, 31 equality constraints
For improved efficiency, Mosek is solving the dual problem.

MOSEK Version 8.0.0.60 (Build date: 2017-3-1 13:09:33)
Copyright © MOSEK ApS, Denmark. WWW: mosek.com
Platform: Windows/64-X86

Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 31
Cones : 6
Scalar variables : 67
Matrix variables : 2
Integer variables : 0

Optimizer started.
Conic interior-point optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 2
Eliminator terminated.
Eliminator - tries : 1 time : 0.00
Lin. dep. - tries : 1 time : 0.00
Lin. dep. - number : 0
Presolve terminated. Time: 0.01
Optimizer - threads : 6
Optimizer - solved problem : the primal
Optimizer - Constraints : 19
Optimizer - Cones : 6
Optimizer - Scalar variables : 57 conic : 56
Optimizer - Semi-definite variables: 2 scalarized : 172
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 : 184 after factor : 190
Factor - dense dim. : 0 flops : 6.47e+004
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 4.0e+000 4.1e+003 1.0e+000 0.00e+000 6.400082949e+002 0.000000000e+000 1.0e+000 0.05
1 1.6e+000 1.7e+003 2.7e-001 -1.00e+000 -2.376025917e+004 -1.996351657e+002 4.0e-001 0.16
2 3.8e-001 3.9e+002 3.0e-002 -9.99e-001 -1.565681401e+005 -1.557348051e+003 9.5e-002 0.16
3 5.7e-002 5.8e+001 1.8e-003 -9.95e-001 -1.120029907e+006 -1.339634576e+004 1.4e-002 0.17
4 1.2e-002 1.3e+001 1.9e-004 -9.65e-001 -4.762713122e+006 -6.469740899e+004 3.1e-003 0.17
5 2.7e-003 2.8e+000 2.4e-005 -8.36e-001 -1.426353304e+007 -2.362499226e+005 6.7e-004 0.19
6 5.3e-004 5.5e-001 6.4e-006 -1.84e-001 -7.961201621e+006 -3.747400108e+005 1.3e-004 0.20
7 1.7e-004 1.8e-001 1.1e-005 1.36e+000 -4.986274873e+005 -2.319884747e+005 4.3e-005 0.20
8 8.3e-005 8.5e-002 1.3e-005 3.40e+000 -5.514590164e+004 -6.513286683e+003 2.1e-005 0.22
9 4.4e-005 4.5e-002 1.0e-005 2.26e+000 1.925479118e+004 3.944779616e+004 1.1e-005 0.23
10 1.9e-005 2.0e-002 7.3e-006 1.59e+000 3.615021470e+004 4.381128752e+004 4.8e-006 0.23
11 7.9e-006 8.1e-003 5.4e-006 1.42e+000 4.661034278e+004 4.895717167e+004 2.0e-006 0.25
12 5.5e-006 5.6e-003 4.0e-006 9.23e-001 4.691438907e+004 4.897774644e+004 1.4e-006 0.25
13 1.2e-006 1.2e-003 3.0e-006 1.29e+000 5.072978145e+004 5.091674736e+004 3.0e-007 0.27
14 5.1e-007 5.2e-004 1.6e-006 9.80e-001 5.093321918e+004 5.104134693e+004 1.3e-007 0.28
15 1.2e-007 1.2e-004 1.0e-006 1.22e+000 5.124681170e+004 5.126256213e+004 3.0e-008 0.28
16 5.0e-008 5.1e-005 5.8e-007 9.33e-001 5.126855119e+004 5.127651015e+004 1.2e-008 0.28
17 1.4e-008 1.5e-005 3.3e-007 1.18e+000 5.128899916e+004 5.129107109e+004 3.5e-009 0.30
18 5.9e-009 6.1e-006 1.3e-007 5.51e-001 5.128707337e+004 5.128921049e+004 1.5e-009 0.31
19 3.2e-009 2.1e-006 2.8e-008 -5.41e-001 5.127644215e+004 5.128226048e+004 5.0e-010 0.31
20 2.2e-009 8.9e-007 1.0e-008 -4.27e-001 5.123020413e+004 5.123806012e+004 2.1e-010 0.33
21 1.4e-009 4.1e-007 4.6e-009 -2.83e-001 5.115758279e+004 5.116588873e+004 9.8e-011 0.33
22 5.6e-010 1.9e-007 2.8e-009 2.91e-001 5.106152839e+004 5.106624913e+004 4.6e-011 0.34
23 2.9e-010 9.6e-008 1.4e-009 1.02e-001 5.099708474e+004 5.100183648e+004 2.3e-011 0.34
24 5.1e-011 1.7e-008 5.5e-010 7.46e-001 5.089299857e+004 5.089401089e+004 4.1e-012 0.36
25 6.5e-012 2.2e-009 1.8e-010 8.47e-001 5.086327638e+004 5.086343903e+004 5.3e-013 0.38
26 1.2e-011 1.1e-009 1.3e-010 9.77e-001 5.086090488e+004 5.086099016e+004 2.7e-013 0.38
27 1.4e-011 1.1e-009 1.3e-010 1.00e+000 5.086089990e+004 5.086098503e+004 2.7e-013 0.39
28 1.4e-011 1.1e-009 1.3e-010 1.00e+000 5.086089866e+004 5.086098375e+004 2.7e-013 0.41
29 1.4e-011 1.1e-009 1.3e-010 1.00e+000 5.086089835e+004 5.086098343e+004 2.7e-013 0.41
30 1.4e-011 1.1e-009 1.3e-010 1.00e+000 5.086089804e+004 5.086098311e+004 2.7e-013 0.42
31 1.4e-011 1.1e-009 1.3e-010 1.00e+000 5.086089773e+004 5.086098279e+004 2.7e-013 0.42
32 6.8e-012 1.1e-009 1.3e-010 9.96e-001 5.086088784e+004 5.086097257e+004 2.7e-013 0.44
33 1.0e-011 1.1e-009 1.3e-010 1.00e+000 5.086080877e+004 5.086089092e+004 2.6e-013 0.44
34 1.4e-011 1.1e-009 1.3e-010 1.00e+000 5.086079918e+004 5.086088102e+004 2.6e-013 0.45
35 1.3e-011 1.1e-009 1.3e-010 1.00e+000 5.086079858e+004 5.086088040e+004 2.6e-013 0.45
36 1.4e-011 1.1e-009 1.3e-010 1.00e+000 5.086079798e+004 5.086087978e+004 2.6e-013 0.47
37 1.4e-011 1.1e-009 1.3e-010 1.00e+000 5.086079679e+004 5.086087855e+004 2.6e-013 0.47
38 1.4e-011 1.1e-009 1.3e-010 1.00e+000 5.086079664e+004 5.086087840e+004 2.6e-013 0.48
39 1.4e-011 1.1e-009 1.3e-010 1.00e+000 5.086079634e+004 5.086087809e+004 2.6e-013 0.48
40 1.4e-011 1.1e-009 1.3e-010 1.00e+000 5.086079619e+004 5.086087793e+004 2.6e-013 0.50
41 1.4e-011 1.1e-009 1.3e-010 1.00e+000 5.086079560e+004 5.086087732e+004 2.6e-013 0.52
42 1.4e-011 1.1e-009 1.3e-010 1.00e+000 5.086079500e+004 5.086087670e+004 2.6e-013 0.52
43 1.4e-011 1.1e-009 1.3e-010 1.00e+000 5.086079500e+004 5.086087670e+004 2.6e-013 0.52
Interior-point optimizer terminated. Time: 0.53.

Optimizer terminated. Time: 0.58

Interior-point solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : NEAR_OPTIMAL
Primal. obj: 5.0860795001e+004 nrm: 4e+007 Viol. con: 1e-004 var: 6e-003 barvar: 0e+000 cones: 0e+000
Dual. obj: 5.0860876703e+004 nrm: 6e+004 Viol. con: 0e+000 var: 4e-004 barvar: 2e-007 cones: 0e+000
Optimizer summary
Optimizer - time: 0.58
Interior-point - iterations : 44 time: 0.53
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

Mosek error: MSK_RES_TRM_STALL ()

Status: Inaccurate/Solved
Optimal value (cvx_optval): -50860.9

t1 =

4.4079e+04 - 8.1318e-10i

t2 =

 1

The output of t1 and t2 doesn’t match what you showed earlier.

Mosek did not solve to the desired tolerance. Nevertheless, I don’t see how that would result in the t2 value you show. Perhaps square_pos got corrupted.

Given your use of Mosek 8.0.0.60, it seems likely you are using CVX 2.1. I recommend you delete all CVX directories from your MATLAB path, then start a new MATLAB session, and install CVX 2.2. You will then have Mosek 9.1.something. If you download Mosek 9.2.x from the Mosek site, then choose that version of Mosek, which you can see from cvx_solver. Or before installing CVX 2.2, rename the mosek directory under the CVX directory to something else - then CVX won’t find it, and you will have only the version of Mosek you downloaded, so can just specify cvx_solver mosek, rather than cvx_solver Mosek_2 or whatever.

OK, thank you Mark for you patience and help. I’ll have a try.

I installed cvx2.2, but it seems doesn’t work for my problem.
image

Calling Mosek 9.1.9: 167 variables, 31 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 : 31
Cones : 6
Scalar variables : 67
Matrix variables : 2
Integer variables : 0

Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 2
Eliminator terminated.
Eliminator - tries : 1 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 : 31
Cones : 6
Scalar variables : 67
Matrix variables : 2
Integer variables : 0

Optimizer - threads : 6
Optimizer - solved problem : the primal
Optimizer - Constraints : 19
Optimizer - Cones : 6
Optimizer - Scalar variables : 57 conic : 56
Optimizer - Semi-definite variables: 2 scalarized : 172
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 : 184 after factor : 190
Factor - dense dim. : 0 flops : 6.47e+04
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 3.2e+02 1.0e+06 7.0e+00 0.00e+00 5.000379109e+00 -1.000000000e+00 1.0e+00 0.03
1 1.5e+02 4.9e+05 4.8e+00 -1.00e+00 2.514165073e+00 -2.324738894e+00 4.6e-01 0.11
2 3.3e+01 1.1e+05 2.3e+00 -1.00e+00 -1.521187190e+01 -1.257561415e+01 1.0e-01 0.11
3 5.0e+00 1.7e+04 8.8e-01 -1.00e+00 -1.570619732e+02 -1.007266956e+02 1.6e-02 0.11
4 1.1e+00 3.6e+03 4.1e-01 -1.00e+00 -7.935873698e+02 -5.112220118e+02 3.5e-03 0.11
5 2.4e-01 7.9e+02 1.9e-01 -9.99e-01 -3.804281156e+03 -2.481866377e+03 7.5e-04 0.13
6 5.0e-02 1.7e+02 8.8e-02 -9.97e-01 -1.816933896e+04 -1.194071162e+04 1.6e-04 0.13
7 9.3e-03 3.1e+01 3.7e-02 -9.86e-01 -9.396112106e+04 -6.194791716e+04 2.9e-05 0.13
8 4.6e-03 1.5e+01 2.2e-02 -8.21e-01 -1.277867781e+05 -8.254318154e+04 1.5e-05 0.13
9 2.8e-03 9.4e+00 7.8e-03 6.45e-01 -2.209806435e+04 -6.571195434e+03 9.0e-06 0.14
10 1.3e-03 4.3e+00 2.2e-03 7.43e-01 1.464638187e+04 2.073647132e+04 4.1e-06 0.14
11 5.8e-04 1.9e+00 6.8e-04 1.02e+00 3.317949207e+04 3.598698077e+04 1.8e-06 0.14
12 1.6e-04 5.4e-01 1.1e-04 1.06e+00 3.999012913e+04 4.085263849e+04 5.1e-07 0.14
13 5.1e-05 1.7e-01 1.9e-05 1.09e+00 4.308746442e+04 4.336089313e+04 1.6e-07 0.14
14 2.4e-05 7.9e-02 6.3e-06 9.48e-01 4.375905009e+04 4.390292842e+04 7.5e-08 0.16
15 5.5e-06 1.8e-02 5.7e-07 1.25e+00 4.439602605e+04 4.441747984e+04 1.8e-08 0.16
16 2.1e-06 6.8e-03 1.4e-07 1.02e+00 4.447779134e+04 4.448657135e+04 6.5e-09 0.16
17 1.5e-07 5.1e-04 1.9e-09 1.26e+00 4.453268085e+04 4.453299079e+04 4.9e-10 0.16
18 8.9e-12 2.9e-08 6.4e-13 1.01e+00 4.453482092e+04 4.453482187e+04 2.5e-12 0.17
19 2.7e-12 5.1e-10 3.5e-13 1.00e+00 4.453473541e+04 4.453473540e+04 8.9e-15 0.17
Optimizer terminated. Time: 0.19

Interior-point solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: 4.4534735407e+04 nrm: 8e+04 Viol. con: 3e-06 var: 1e-06 barvar: 0e+00 cones: 7e-11
Dual. obj: 4.4534735392e+04 nrm: 6e+04 Viol. con: 0e+00 var: 3e-06 barvar: 8e-12 cones: 0e+00
Optimizer summary
Optimizer - time: 0.19
Interior-point - iterations : 19 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: Solved
Optimal value (cvx_optval): -44534.7

t1 =

4.3436e+04 + 1.0236e-08i

t2 =

 1

Start a fresh session of MATLAB. Copy and paste your code into the command window and show the output in that window.

You apparently are running a different code than what was in your post which is what I ran. Your lack of configuration control does not serve to your advantage, or economical use of my time.

image

Whar is the output of
which -all square_pos

Here is mine:

>> which -all square_pos
C:\cvx_2.2_1148\functions\square_pos.m
C:\cvx_2.2_1148\functions\@cvx\square_pos.m  % cvx method

Same as you.

Results from
which -all square

Mine are:

>> which -all square
C:\cvx_2.2_1148\functions\square_\square.m
C:\cvx_2.2_1148\functions\@cvx\square.m     % cvx method

I suspect you have another version of square which is causing the wrong result. Perhas this from Signal Processing Toolbox https://www.mathworks.com/help/signal/ref/square.html .

Here is the square_pos at ```
C:\cvx_2.2_1148\functions\square_pos.m

function y = square_pos( x )

%SQUARE_POS Square of positive part.
% SQUARE_POS(X) is the square of the postive parts of the elements of X;
% i.e., SQUARE_POS(X)=MAX(X,0).^2. X must be real.
%
% Disciplined convex programming information:
% SQUARE_POS(X) is convex and nondecreasing in X. Thus when used in
% CVX expressions, X must be convex (or affine).

narginchk(1,1);
if ~isreal( x ),
error( ‘Argument must be real.’ );
end

y = square( max( x, 0 ) );

% Copyright 2005-2016 CVX Research, Inc.
% See the file LICENSE.txt for full copyright information.
% The command ‘cvx_where’ will show where this file is located.

but square(x) and square_pos(x) are two different function.

square_pos calls square,in your case, the Signal Processing Toolbox version,

The version of square_pos called for CVX arguments will not encounter this. You could just avoid calling square_pos with numerical arguments, because it is not necessary, anyway. norm(...,,'fro')^2 works just fine for numerical arguments.

Here is the definitive word on the subject. Read the full thread, not just the portion displayed below.

I see, thank you very much Mark.