Global Optimization for the Sum of Concave-Convex Ratios Problem

Abstract EN

This paper presents a branch and bound algorithm for globally solving the sum of concave-convex ratios problem (P) over a compact convex set.

Firstly, the problem (P) is converted to an equivalent problem (P1).

Then, the initial nonconvex programming problem is reduced to a sequence of convex programming problems by utilizing linearization technique.

The proposed algorithm is convergent to a global optimal solution by means of the subsequent solutions of a series of convex programming problems.

Some examples are given to illustrate the feasibility of the proposed algorithm.