One of the conditions is ignored, thus resulting to inappropriate values


I have written the following code, aiming to find the optimum values of p(1), p(2), l(1), l(2) and r(1), r(2) in order to minimize the sum of zC^3pow_p(l,3)/T^2+p*T. However, the constraint for r(2) is not satisfied, therefore resulting in wrong values. Could please someone provide some help, in what might be wrong with my code? My code is provided below:

B_sub = 200000;	
L = 10^5;      
z = 10^-12;    
C = 10;          
T = 1;          

                variable p(2)
                variable l(2)
                variable r(2)

                minimize sum(z*C^3*pow_p(l,3)/T^2+p*T)

                subject to
                    r >= (L-l)/(B_sub*T)    % Rate constraint
                    p >= 0                        % Power constraint (low)
                    p <= z*C^3*L^3/T^3   % Power constraint (high)
                    l >= 0                          % Local data constraint (low)
                    l <= L                          % Local data constraint (high)

                    % MAC contraints
                    r(1) <= -rel_entr(1,1+p(1)*norm(CG(uiid(1)))^2/(d(uiid(1))^4))/0.6931
                    r(2) <= -rel_entr(1,1+p(2)*norm(CG(uiid(2)))^2/(d(uiid(2))^4))/0.6931
                    r(1)+r(2) <= -rel_entr(1,1+p(1)*norm(CG(uiid(1)))^2/(d(uiid(1))^4)+p(2)*norm(CG(uiid(2)))^2/(d(uiid(2))^4))/0.6931

In addition, the final result is Inaccurate/Solved, i know this might result in not accurate values, but the results I are way off for just the value of r(2).

Also, can I have an equality constraint in my optimization problem?
i.e. l == L-r*B_sub*T, where l and r are parameters need to be found

I know it’s a lot, but any advice or suggestion would be very much appreciated.

(Mark L. Stone) #2

You have not provided a reproducible problem. uiid is not provided.

You don’t seem to have taken the suggestions from your previous thread What is causing the final Status: Inaccurate/Solved? and how can I modify my code to get it Solved? fully to heart. Extremely large and non-zero small magnitude numbers are causing great difficulty for the solver, with possibly adverse consequences such as incorrect feasibility determination, and not satisfying constraints.

For instance, you have a constraint which evaluates to p <= 1e+06. That could cause difficulty for the solver. The first term in the objective function evaluates to 1e-09 * pow_p(l,3). And you are adding to that another term equal to p. So this may also cause great difficulty for the solver. I will let you figure out how to fic this up, which might require changes to your model beyond just re-scaling.

Equality constraints are allowed in CVX only if they are affine, which your example appears to be.