P(i) = real(G(i))+F(i) should be P(i) == real(G(i))+F(i). pls read the,cvx users’ guide.

This error is like this, P is an expression about Q, it is not a number.

function [Q_,P_] = CVX_theta_Optimal(M,P_max,K,Z,v,q,p,BER)

cvx_begin

cvx_quiet false;

variable Q(M+1,M+1) hermitian semidefinite

variable P(K)

```
expression F(K)
expression G(K)
expression G_gradient
expression A(K)
for i=1:K
if i == 1
s_inter = 0;
G_tmp = 0;
else
for j=1:i-1
s_inter = p(j).*(trace(Z(:,:,j)*q)+ norm((v(:,j)))) + s_inter;
G_tmp = G_tmp + Z(:,:,j)';
end
end
G_gradient = G_tmp/log(2)*(s_inter+1);
G(i) = log(real(s_inter+1))+2*real(trace(G_gradient.'*(Q-q)))/log(2);
F(i) = -log(real(trace(Z(:,:,i)*Q)+norm(v(:,i))))/log(2);
end
```

% expression N

%

% norm_grad = two_norm_grad(q);

% N = norm_nuc(Q)-norm(q)+2*real(trace(norm_grad*norm_grad’*(Q-q)));

%

minimize sum§

subject to

for i=1:K

0<P(i)<=P_max;

end

diag(Q) == 1 ;

for i = 1:K

A(i) = 2.^((real(real(G(i))+F(i))+log(power((5.5+sqrt(1/200)*qfuncinv(BER)/log(2)),2)-1)/log(2)));

A(i)<=P(i);

end

% N = 0;

cvx_end

I change my code to this ,but this solution is very small,it not satisfy this constraint.

Follow the instructions at CVXQUAD: How to use CVXQUAD's Pade Approximant instead of CVX's unreliable Successive Approximation for GP mode, log, exp, entr, rel_entr, kl_div, log_det, det_rootn, exponential cone. CVXQUAD's Quantum (Matrix) Entropy & Matrix Log related functions .

function [Q_,P_] = CVX_theta_Optimal(M,P_max,K,Z,v,q,p,BER)

cvx_begin

cvx_quiet false;

variable Q(M+1,M+1) hermitian semidefinite

variable P(K)

expression F(K)

expression G(K)

for i=1:K

if i == 1

s_inter = 0;

G_tmp = 0;

else

for j=1:i-1

s_inter = p(j).*(trace(Z(:,:,j) q)+ norm((v(:,j)))) + s_inter;
G_tmp = G_tmp + Z(:,:,j)’;
end
end
G_gradient = G_tmp/log(2)(s_inter+1);
G(i) = -rel_entr(1,real(s_inter+1))+2*real(trace(G_gradient.’

*(Q-q)))/log(2);*

F(i) = -(-rel_entr(1,(real(trace(Z(:,:,i)norm_grad’

F(i) = -(-rel_entr(1,(real(trace(Z(:,:,i)

*Q)+norm(v(:,i))))))/log(2);*

end

% expression N

% norm_grad = two_norm_grad(q);

% N = norm_nuc(Q)-norm(q)+2real(trace(norm_gradend

% expression N

% norm_grad = two_norm_grad(q);

% N = norm_nuc(Q)-norm(q)+2

*(Q-q)));*

minimize P(1)+P(2)+P(3)+P(4)

subject to

for i=1:K

0<=P(i)<=P_max;

end

diag(Q) == 1 ;

for i = 1:K

P(i)-exp(log(2)(log(2.^(2+(sqrt(1/200)*qfuncinv(BER)/log(2)))-1)/log(2)+real(real(G(i))+F(i))))>=0;

minimize P(1)+P(2)+P(3)+P(4)

subject to

for i=1:K

0<=P(i)<=P_max;

end

diag(Q) == 1 ;

for i = 1:K

P(i)-exp(log(2)

end

% N = 0;

cvx_end

%Q

P

Q_ = Q;

P_ = P;

end

I change my code to this.Although the optimal value can be generated, it is still not satisfied with the constraint, and the gap is very large. Sometimes NAN also occur.Can you help me see what is the problem?

Thank you !Hope you can help me take a look at this problem.

You haven’t shown us the output. We don’t even know what solution method was used. Note that constrains are not satisfied exactly, but only to within a tolerance. And CVX reported that your problem was solved inaccurately. It is possible that your input data is not well-scaled.

Sorry，This is my code and output.

function [Q_,P_] = CVX_theta_Optimal(M,P_max,K,Z,v,q,p,BER)

cvx_solver mosek

cvx_begin

cvx_quiet false;

variable Q(M+1,M+1) hermitian semidefinite

```
expression F(K)
expression G(K)
expression P(K)
for i=1:K
if i == 1
s_inter = 0;
G_tmp = 0;
else
s_inter = 0;
G_tmp = 0;
for j=1:i-1
s_inter = p(j).*(trace(Z(:,:,j)*q)+ sum(abs(v(:,i)).^2)) + s_inter;
G_tmp = G_tmp + Z(:,:,j).';
end
end
G_gradient = G_tmp/log(2)*(s_inter+1);
G(i) = real((s_inter+1))/log(2)+2*real(trace(G_gradient.'*(Q-q)));
F(i) = -(-rel_entr(1,(real(trace(Z(:,:,i)*Q)+sum(abs(v(:,i)).^2)))))/log(2);
end
%expression N
%norm_grad = two_norm_grad(q);
%N = norm_nuc(Q)-norm(q)+2*real(trace(norm_grad*norm_grad'*(Q-q)));
minimize sum(P)
subject to
diag(Q) == 1 ;
for i=1:K
0<=P(i)<=P_max;
end
for i=1:K
P(i)-exp(log(2)*(log(2.^(1+(sqrt(1/200)*qfuncinv(BER)/log(2)))-1)/log(2)+real(G(i)+F(i))))>=0;
end
%N = 0;
```

cvx_end

%Q

P

Q_ = Q;

P_ = P;

## end

Successive approximation method to be employed.

Mosek will be called several times to refine the solution.

Original size: 8551 variables, 89 equality constraints

8 exponentials add 56 variables, 32 equality constraints

## Cones | Errors |

Mov/Act | Centering Exp cone Poly cone | Status

--------±--------------------------------±--------

0/ 2 | 8.000e+00 6.868e+02 3.299e+43 | Infeasible

Status: Infeasible

Optimal value (cvx_optval): +Inf

P =

NaN

NaN

NaN

NaN

I don’t know why this problem occurs. I don’t know how to modify my code to make it run normally. Please help me, thank you!!!

Sorry，This is my code and output.

Follow the advice in the link in my previous post.

if the problem is still reported infeasible, follow the advice (except for section 1) at https://yalmip.github.io/debugginginfeasible .

Thank you very much！

Actually, as I wrote in the other thread, make sure you are using CVX 2.2 and Mosek 9.x. Otherwise you would not be getting the output with Cones | Errors … which shows the Successive approximation method was used.

OK，Thank you！I change my CVX version.

I have another question, when should I use cvx_quad?

As long as your problem can reformulated using the exponential cone and symmetric cones you should not use it.

Thank you very much!

I have another question that needs your help

When I solving the SOCP problem, the output is Nan?

this my problem

This is my code and output.

%% 参数

clc;clear ;

Z_mc=1;

c=3e8;

f =28e9;%f=18.5e+9; 8e-3=0.008 0.5lambda

lambda=c/f;

dx=5e-3;% 0.5lambda

dy=dx;

Ny=8;Nx=8;

kc=1j *2 *pi /lambda;

theta_0=0;%目标角度 *pi/180

phi_0=0;

% theta_i=30;%干扰角度 *pi/180

% phi_i=0;

% INR=30;

u=10.^(1./10);%主瓣阈值（上限）

l=10.^(-1./10);%主瓣阈值（下限）

taos=0.001;%旁瓣阈值（上限）30dB taos=0.001;%旁瓣阈值（上限）=10.^(-30./10); -30db

%% 目标导向矢量

a0_x=exp(kc *(0:Nx-1)’ *dx *sin(theta_0 *pi/180) *cos(phi_0 *pi/180));

a0_y=exp(kc *(0:Ny-1)’ *dy *sin(theta_0 *pi/180) *sin(phi_0 pi/180));

a0=kron(a0_x, a0_y);%导向矢量

a=a0’ Z_mc;%耦合导向矢量 1N

%% 主瓣导向矢量

theta_m=(-10:10);

phi_m=(-10:10);

M =length(theta_m);

for m=1:M

am_x=exp(kc * (0:Nx-1)’ * dx * sin(theta_m(m) * pi/180) * cos(phi_m(m) * pi/180));

am_y=exp(kc * (0:Ny-1)’ * dy * sin(theta_m(m) * pi/180) * sin(phi_m(m) * pi/180));

a10=kron(am_x, am_y);%导向矢量

a1(m,:)=a10’ * Z_mc;%耦合导向矢量 1N

end

%% 旁瓣导向矢量

theta_s=[-91:4:-9,11:4:91];

phi_s=[-91:4:-9,11:4:91];

S =length(theta_s);

for s=1:S

as_x=exp(kc * (0:Nx-1)’ * dx * sin(theta_s(s) * pi/180) * cos(phi_s(s) pi/180));

as_y=exp(kc * (0:Ny-1)’ * dy * sin(theta_s(s) * pi/180) * sin(phi_s(s) * pi/180));

a20=kron(as_x, as_y);%导向矢量

a2(s,:)=a20’ * Z_mc;%耦合导向矢量 1N

end

N=Ny * Nx;

%% cvx

yita=(u-l) * sqrt(Ny * Nx)/2;%导向矢量误差

cvx_begin

cvx_solver SeDuMi

variable w(N) complex %N1

minimize(norm(w))%优化目标

subject to

a * w==1;

for m=1:1:M

real(a1(m, : ) * w) -yita * norm(w) >= l;%

norm(a1(m, : ) * w)+yita * norm(w) <= u;%

end

for s=1:1:S

norm(a2(s,: ) * w) +yita * norm(w)<= taos;%

end

cvx_end

% wopt=w% N1