I met some problem in optimization problem
my code is
while(error1 > epsilon && error2 > epsilon && r1 < r_max)
e_old = ones(M,1);
lambda = 10; lambda_max = 1000;
rho_old = [1,1,1];
a_old = [1;1;1];
for k = 1:K
mu_1(k) = 1/(rho_old(k) +1);
m11(k) = 1/(1+a_old(k)*p(k));
end
cvx_begin sdp
cvx_solver mosek
variables e(M,1) b(M,1) c(M,1) mu_e(1,K) mu_g(1,K) kappa(1,K) ...
a(1,K) rho(1,K) d(1,K)
expression ex(1,K)
obj =sum(kappa) + lambda*(sum(b) + sum(c)); %
maximize obj
subject to
for k = 1:K
[a(k) - M*mu_g(k) - mu_e(k) (H_UE(:,k) + H_IE*diag(H_UI(:,k))*e)'; ...
(H_UE(:,k) + H_IE*diag(H_UI(:,k))*e) ones(E,E) ]>=0;
mu_g(k)>=0;
mu_e(k)>=0;
log(rho(k) + d(k) +1) - mu_1(k)*(rho(k)+1) + log(mu_1(k)) + 2 - m11(k)*(a(k)*p(k)+1) + log(m11(k)) >= r(k) + kappa(k);
p(k)*(2*real((H_UB(:,k)'+e_old'*H(:,:,k)')*W(:,k)*W(:,k)'*(H_UB(:,k)+H(:,:,k)*e))) - abs((H_UB(:,k)'+e_old'*H(:,:,k)')*W(:,k))^2 >= d(k);
for j = k+1:K
ex(j) = p(j)*abs((H_UB(:,j)'+e_old'*H(:,:,j)')*W(:,k))^2;
% ex(j) = p(j)*(2*real((H_UB(:,j)'+e_old'*H(:,:,j)')*W(:,k)*W(:,k)'*(H_UB(:,j)+H(:,:,j)*e))) - abs((H_UB(:,j)'+e_old'*H(:,:,j)')*W(:,k))^2;
end
sum(ex)<= rho(k);
for m = 1:M
2*real(e_old(m)*e(m))- abs(e_old(m))^2 >= 1 - b(m);
e(m)*conj(e(m)) <= 1 + c(m)
end
end
cvx_end
error1 = sum(c) + sum(b);
error2 = norm(e-e_old,1); %向量的一范数，各元素绝对值之和
lambda = min(t*lambda,lambda_max);
r1=r1+1;
end
but the result is
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 48
Cones : 18
Scalar variables : 96
Matrix variables : 3
Integer variables : 0
Optimizer started.
Presolve started.
Eliminator - tries : 0 time : 0.00
Lin. dep. - tries : 0 time : 0.00
Lin. dep. - number : 0
Presolve terminated. Time: 0.00
Optimizer terminated. Time: 0.05
Interior-point solution summary
Problem status : PRIMAL_INFEASIBLE
Solution status : PRIMAL_INFEASIBLE_CER
Dual. obj: 1.0000000000e+01 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 barvar: 0e+00 cones: 0e+00
Optimizer summary
Optimizer - time: 0.05
Interior-point - iterations : 0 time: 0.02
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: Unbounded
Optimal value (cvx_optval): +Inf
As we all know, the value of H and W in the above code are about 1. Why the problem is unbounded.