A Deterministic Global Optimization Method for Solving Generalized Linear Multiplicative Programming Problem with Multiplicative Constraints

Abstract

This paper presents a deterministic global optimization algorithm for solving generalized linear multiplicative programming problem with multiplicative constraints (GLMP). By utilizing equivalent transformation and linear relaxation method, a linear relaxation programming (LRP) of equivalent problem (GLMPH) is established. In the algorithm, lower and upper bounds are simultaneously obtained by solving some linear relaxation programming problems (LRP). Global convergence has been proved and results of some sample examples and a small random experiment show that the proposed algorithm is feasible and efficient.