Minimizing the Product of Positive Functions

This paper presents an approach for globally solving the problem of minimizing a product of two finite positive linear functions. Since the product of linear functions need not be convex or quasi-convex thus the given problem may have many local minima which are not a global minimum. The original problem is first reformulated as an equivalent indefinite quadratic problem, then solved through a rectangular branch-and-bound procedure. The computational experiences show the robustness and efficiency of the proposed algorithm.

Keywords:

Global optimization , Branch-and-Bound , Nonconvex optimization