for i =1:10 cvx_begin quiet cvx_solver mosek variable Pi %optimization variables variable Pj variable mu_n nonnegative dual variables nu rho eta phi minimize -(Mn-mu_n.*(1+exp(-an.*(gnx(1,i).*(Pi+Pj)-bn)))) % optimizing Pi and Pj (optimal allocated power) subject to nu: (Pi*hix(1,1))-Omega_i*((Pj.*hix(1,1))+Ni) >= 0; rho: Pi*hjx(1,1)-Omega_j*Nj >= 0; eta: (Pi*hjx(1,1))-Omega_t*((Pj*hjx(1,1))+Nj) >= 0; % Rth = R1 + R2 phi: Gamma_m-qmx(1,i).*(Pi+Pj) >= 0; cvx_end nu = nu+0.1*i; % all dual variables are iteratively increased by step size 0.1 rho = rho+0.1*i; eta = eta+0.1*i; phi = phi+0.1*i; end
No. In any case Mosek will ignore the values if you do.
one more problem with my objective function of “real affine.* log convex”, how to resolved it
If i am using rel_entr, It is not working because it is working for affine and concave.
Leaving side the
-Mn term, which is a constant, the minimum possible objective value appears to be zero, and that is achieved with
mu_n = 0 and any feasible
Pj. Therefore, because
mu_n does not appear in any constraints other than being nonnegative, It looks like
mu_n = 0 is optimal, together with any value of
Pj which satisfy the constraints
Am I missing something?
Log of sigmoid function
You are right sir about taking non-negative parameter value as zero or minimum,