Inner approximation algorithm for generalized linear multiplicative programming problems

Abstract

An efficient inner approximation algorithm is presented for solving the generalized linear multiplicative programming problem with generalized linear multiplicative constraints. The problem is firstly converted into an equivalent generalized geometric programming problem, then some magnifying-shrinking skills and approximation strategies are used to convert the equivalent generalized geometric programming problem into a series of posynomial geometric programming problems that can be solved globally. Finally, we prove the convergence property and some practical application examples in optimal design domain, and arithmetic examples taken from recent literatures and GLOBALLib are carried out to validate the performance of the proposed algorithm.

An Efficient Outer Space Algorithm for Generalized Linear Multiplicative Programming Problem

“…In addition to the branch and bound algorithm mentioned above, some other types of algorithms are also proposed to solve the problem (MP), such as, Phuong and Tuy [21] and Chen and Jiao [22] proposed two monotonic optimization methods for generalized linear fractional programming problem and generalized linear multiplicative programming problems; by utilizing the concept of level set, Liu and Zhao [10] gave a level set method for solving the linear multiplicative programming problem with exponents. Recently, Shen et al [23]- [25] proposed three polynomial time approximation algorithms for generalized linear fractional multiplicative programming problem; Zhao and Zhao [12] presented a convex relaxation method for generalized linear multiplicative programming problem with generalized linear multiplicative constraints; based on geometric programming solver, Zhao and Yang [13] also proposed an inner approximation algorithm for generalized linear multiplicative programming problem with generalized linear multiplicative constraints; Jiao et al [5] formulated an outcome space method for generalized linear multiplicative programming problem with linear constraints; these methods can be also used to solve the problem (MP) considered in this paper.…”