Disciplined convex programming error: Cannot minimize a(n) concave expression

1

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Here is my code.

ap_except0(1,1)=a_ij0(2,1)*p_k0(1,2)+a_ij0(3,1)*p_k0(1,3);
ap_except0(1,2)=a_ij0(1,2)*p_k0(1,1)+a_ij0(3,2)*p_k0(1,3);
ap_except0(1,3)=a_ij0(1,3)*p_k0(1,1)+a_ij0(2,3)*p_k0(1,2);
g_exp0=log2(Cg_k.ap_except0+noise);
fe_exp0=log2(Cg_e(ap_except0+p_k0)+noise);

cvx_solver mosek
cvx_begin

variable p_k(1,3)
expressions g_exp_ub(1,3) fe_exp_ub(1,3) f_exp(1,3) ge_exp(1,3)

g_exp_ub(1,1)=g_exp0(1,1)+...
    Cg_k(1,1)*(a_ij0(2,1)*(p_k(1,2)-p_k0(1,2))+a_ij0(3,1)*(p_k(1,3)-p_k0(1,3)))*log2(exp(1))/...
    (Cg_k(1,1)*ap_except0(1,1)+noise);
g_exp_ub(1,2)=g_exp0(1,2)+...
    Cg_k(1,2)*(a_ij0(1,2)*(p_k(1,1)-p_k0(1,1))+a_ij0(3,2)*(p_k(1,3)-p_k0(1,3)))*log2(exp(1))/...
    (Cg_k(1,2)*ap_except0(1,2)+noise);
g_exp_ub(1,3)=g_exp0(1,3)+...
    Cg_k(1,3)*(a_ij0(1,3)*(p_k(1,1)-p_k0(1,1))+a_ij0(2,3)*(p_k(1,2)-p_k0(1,2)))*log2(exp(1))/...
    (Cg_k(1,3)*ap_except0(1,3)+noise);

sum_ap(1,1)=p_k(1,1)+a_ij0(2,1)*p_k(1,2)+a_ij0(3,1)*p_k(1,3);
sum_ap(1,2)=a_ij0(1,2)*p_k(1,1)+p_k(1,2)+a_ij0(3,2)*p_k(1,3);
sum_ap(1,3)=a_ij0(1,3)*p_k(1,1)+a_ij0(2,3)*p_k(1,2)+p_k(1,3);
sub_ap(1,1)=p_k(1,1)-p_k0(1,1)+a_ij0(2,1)*(p_k(1,2)-p_k0(1,2))+a_ij0(3,1)*(p_k(1,3)-p_k0(1,3));
sub_ap(1,2)=a_ij0(1,2)*(p_k(1,1)-p_k0(1,1))+p_k(1,2)-p_k0(1,2)+a_ij0(3,2)*(p_k(1,3)-p_k0(1,3));
sub_ap(1,3)=a_ij0(1,3)*(p_k(1,1)-p_k0(1,1))+a_ij0(2,3)*(p_k(1,2)-p_k0(1,2))+p_k(1,3)-p_k0(1,3);

fe_exp_ub(1,1)=1-(Cg_e*(p_k0(1,1)+a_ij0(2,1)*p_k0(1,2)+a_ij0(3,1)*p_k0(1,3))+noise)...
    *pow_p(Cg_e*(p_k(1,1)+a_ij0(2,1)*p_k(1,2)+a_ij0(3,1)*p_k(1,3))+noise,-1);

fe_exp_ub(1,2)=1-(Cg_e*(a_ij0(1,2)*p_k0(1,1)+p_k0(1,2)+a_ij0(3,2)*p_k0(1,3))+noise)...
    *pow_p(Cg_e*(a_ij0(1,2)*p_k(1,1)+p_k(1,2)+a_ij0(3,2)*p_k(1,3))+noise,-1);

fe_exp_ub(1,3)=1-(Cg_e*(a_ij0(1,3)*p_k0(1,1)+a_ij0(2,3)*p_k0(1,2)+p_k0(1,3))+noise)...
    *pow_p(Cg_e*(a_ij0(1,3)*p_k(1,1)+a_ij0(2,3)*p_k(1,2)+p_k(1,3))+noise,-1);

f_exp(1,1)=log(2).*(Cg_k(1,1).*(p_k(1,1)+a_ij0(2,1)*p_k(1,2)+a_ij0(3,1)*p_k(1,3))+noise);
f_exp(1,2)=log(2).*(Cg_k(1,2).*(a_ij0(1,2)*p_k(1,1)+p_k(1,2)+a_ij0(3,2)*p_k(1,3))+noise);
f_exp(1,3)=log(2).*(Cg_k(1,3).*(a_ij0(1,3)*p_k(1,1)+a_ij0(2,3)*p_k(1,2)+p_k(1,3))+noise);

ge_exp(1,1)=log(2).*(Cg_e*(a_ij0(2,1)*p_k(1,2)+a_ij0(3,1)*p_k(1,3))+noise);
ge_exp(1,2)=log(2).*(Cg_e*(a_ij0(1,2)*p_k(1,1)+a_ij0(3,2)*p_k(1,3))+noise);
ge_exp(1,3)=log(2).*(Cg_e*(a_ij0(1,3)*p_k(1,1)+a_ij0(2,3)*p_k(1,2))+noise);

result=0;
for k=1:K
    result=result+g_exp_ub(1,k)-f_exp(1,k)-ge_exp(1,k)+fe_exp_ub(1,k);
end


minimize result
subject to 
    p_k >= 0;
    sum(p_k) <= P_max;

cvx_end

My problem is that CVX thinks my objective function is concave.
But from the optimization problem in the graph, the objective function is convex.

2

Try add “expressions result” into your code. Because result is an expression too. And you initialize it as 0, if you don’t declare it expression, it might go wrong.

3

I tried your suggestion. But cvx still shows it’s concave.

4

Please show your output.

5

This is my output.

错误使用 cvxprob/newobj (line 57)
Disciplined convex programming error:
Cannot minimize a(n) concave expression.

出错 minimize (line 21)
newobj( prob, ‘minimize’, x );

出错 Algorithm3 (line 71)
minimize result3

6

I changed my code.

ap_except0(1,1)=a_ij0(2,1)*p_k0(1,2)+a_ij0(3,1)*p_k0(1,3);
ap_except0(1,2)=a_ij0(1,2)*p_k0(1,1)+a_ij0(3,2)*p_k0(1,3);
ap_except0(1,3)=a_ij0(1,3)*p_k0(1,1)+a_ij0(2,3)*p_k0(1,2);
g_exp0=log2(Cg_k.ap_except0+noise);
fe_exp0=log2(Cg_e(ap_except0+p_k0)+noise);

cvx_solver mosek
cvx_begin

variable p_k(1,3)
expressions g_exp_ub(1,3) fe_exp_ub(1,3) f_exp(1,3) ge_exp(1,3) result3

g_exp_ub(1,1)=(1-(Cg_k(1,1)*ap_except0(1,1)+noise)...
    *pow_p(Cg_k(1,1)*(a_ij0(2,1)*p_k(1,2)+a_ij0(3,1)*p_k(1,3))+noise,-1))*log(2)*exp(1);
g_exp_ub(1,2)=(1-(Cg_k(1,2)*ap_except0(1,2)+noise)...
    *pow_p(Cg_k(1,2)*(a_ij0(1,2)*p_k(1,1)+a_ij0(3,2)*p_k(1,3))+noise,-1))*log(2)*exp(1);
g_exp_ub(1,3)=(1-(Cg_k(1,3)*ap_except0(1,3)+noise)...
    *pow_p(Cg_k(1,3)*(a_ij0(1,3)*p_k(1,1)+a_ij0(2,3)*p_k(1,2))+noise,-1))*log(2)*exp(1);


sum_ap(1,1)=p_k(1,1)+a_ij0(2,1)*p_k(1,2)+a_ij0(3,1)*p_k(1,3);
sum_ap(1,2)=a_ij0(1,2)*p_k(1,1)+p_k(1,2)+a_ij0(3,2)*p_k(1,3);
sum_ap(1,3)=a_ij0(1,3)*p_k(1,1)+a_ij0(2,3)*p_k(1,2)+p_k(1,3);
sub_ap(1,1)=p_k(1,1)-p_k0(1,1)+a_ij0(2,1)*(p_k(1,2)-p_k0(1,2))+a_ij0(3,1)*(p_k(1,3)-p_k0(1,3));
sub_ap(1,2)=a_ij0(1,2)*(p_k(1,1)-p_k0(1,1))+p_k(1,2)-p_k0(1,2)+a_ij0(3,2)*(p_k(1,3)-p_k0(1,3));
sub_ap(1,3)=a_ij0(1,3)*(p_k(1,1)-p_k0(1,1))+a_ij0(2,3)*(p_k(1,2)-p_k0(1,2))+p_k(1,3)-p_k0(1,3);

fe_exp_ub(1,1)=(1-(Cg_e*(p_k0(1,1)+a_ij0(2,1)*p_k0(1,2)+a_ij0(3,1)*p_k0(1,3))+noise)...
    *pow_p(Cg_e*(p_k(1,1)+a_ij0(2,1)*p_k(1,2)+a_ij0(3,1)*p_k(1,3))+noise,-1))*log(2)*exp(1);

fe_exp_ub(1,2)=(1-(Cg_e*(a_ij0(1,2)*p_k0(1,1)+p_k0(1,2)+a_ij0(3,2)*p_k0(1,3))+noise)...
    *pow_p(Cg_e*(a_ij0(1,2)*p_k(1,1)+p_k(1,2)+a_ij0(3,2)*p_k(1,3))+noise,-1))*log(2)*exp(1);

fe_exp_ub(1,3)=(1-(Cg_e*(a_ij0(1,3)*p_k0(1,1)+a_ij0(2,3)*p_k0(1,2)+p_k0(1,3))+noise)...
    *pow_p(Cg_e*(a_ij0(1,3)*p_k(1,1)+a_ij0(2,3)*p_k(1,2)+p_k(1,3))+noise,-1))*log(2)*exp(1);



f_exp(1,1)=log(2).*(Cg_k(1,1).*(p_k(1,1)+a_ij0(2,1)*p_k(1,2)+a_ij0(3,1)*p_k(1,3))+noise);
f_exp(1,2)=log(2).*(Cg_k(1,2).*(a_ij0(1,2)*p_k(1,1)+p_k(1,2)+a_ij0(3,2)*p_k(1,3))+noise);
f_exp(1,3)=log(2).*(Cg_k(1,3).*(a_ij0(1,3)*p_k(1,1)+a_ij0(2,3)*p_k(1,2)+p_k(1,3))+noise);

ge_exp(1,1)=log(2).*(Cg_e*(a_ij0(2,1)*p_k(1,2)+a_ij0(3,1)*p_k(1,3))+noise);
ge_exp(1,2)=log(2).*(Cg_e*(a_ij0(1,2)*p_k(1,1)+a_ij0(3,2)*p_k(1,3))+noise);
ge_exp(1,3)=log(2).*(Cg_e*(a_ij0(1,3)*p_k(1,1)+a_ij0(2,3)*p_k(1,2))+noise);

result3=0;
for k=1:K
    result3=result3+g_exp_ub(1,k)-f_exp(1,k)-ge_exp(1,k)+fe_exp_ub(1,k);
end

minimize result3
subject to 
    p_k >= 0;
    sum(p_k) <= P_max;

cvx_end

7

You didn’t provide your data. So I guess some data are <= 0 that are expected to be >= 0. You need to check that. By the way, I have an another bold guess: p_k0 rather than p_k should be inside pow_p() ??

8

Thank you very much. That’s what you suspect. My problem has been solved.