Date: Jan 19, 2013 2:23 AM
Author: Muhammad
Subject: Lower bound of a non-convex program through the dual problem in Matlab
I want to get the lower bound of a non-convex program through the dual problem. Can I do it using the standard Matlab optimization toolboxes?

For example, I have the following problem:

min f0(x)

s.t. f1(x) <= 0

Here, f1(x) is non-convex. Let, the lagrange dual function, g(p) = inf_x (f0(x) + p*f1(x).

The optimal dual solution: max_p g(p). This dual solution is a lower bound of my original primal problem.

Can I obtain this dual solution, i.e., the lower bound, using Matlab optimization toolboxes? I know that I cannot get the global minimum through the primal problem since it is non-convex. Any help will be appreciated.

Thanks,

Nazmul