An outcome-space normal cone method for generalized concave multiplicative problems

Tóm tắt báo cáo

Generalized Multiplicative programming problems have important applications in areas such as engineering, finance, economics, VLSI chip design and other fields. Although they are NP-hard global optimization problems, even for the case that the feasible set is a polytope and the objective function is the product of linear functions, they have attracted a lot of attention from researchers and practitioners.

This paper addresses an outcome-space outer approximation algorithm for solving the problem of globally maximizing the sum of products of concave functions over a nonempty convex compact set. From the relationship between normal cones in decision space and ones in outcome space, the approximate cutting-planes are established by solving the systems of linear equations which lead the computational efficiency of the proposed algorithm. Some illustrative examples are given and the numerical experiments are reported.