If dual variables are non negative, Is there need to initialized?


(Neelu Gupta) #1
  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

(Erling D.Andersen) #2

No. In any case Mosek will ignore the values if you do.


(Neelu Gupta) #3

okay, Thankyou
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.


(Mark L. Stone) #5

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 Pi and 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 Pi and Pj which satisfy the constraints

Am I missing something?


Log of sigmoid function
(Neelu Gupta) #6

You are right sir about taking non-negative parameter value as zero or minimum,