Feasibility_problem_CVX

1

To whom it may concern,

I am trying to solve a quasiconvex optimization problem through bisection. I tried to adapt the formulation from section 5.1 (http://stanford.edu/~boyd/papers/pdf/magdes_cdc96.pdf). For that problem, if I fix N, and then just run the problem in CVX (for the fixed instance), it solves the problem and returns a solution vector. I am trying to understand what other properties does that solution vector have.

In my actual problem, I am trying to optimize power while fixing different time instants, that is:

min_{P_1, P_2, P_3} 0
s.t. P_1 + P_2 + P_3 <= P_sum
.
. (more cvx constrains)
.

If I add extra convex constrains (like the sum power constraint above), would it return the vector that guarantees feasibility, and at the same time results in most savings in sum power? If not, what point would the solution of this problem return?

I hope my question is clear,
Thanks for your time!

2

Emply the bisection algorithm as described in “Quasiconvex optimization via convex feasibility problems” in section 4.2.5 of “Convex Optimization”, by Boyd and Vandenberghe (two of the three authors of the paper you linked) http://web.stanford.edu/~boyd/cvxbook/

3

Thanks for the info!