A nonisolated optimal solution of general linear multiplicative programming problems

This article presents a finite branch-and-bound algorithm for globally solving general linear multiplicative programming problems (GLMP). The proposed algorithm is based on the recently developed theory of monotonic optimization. The proposed algorithm provides a nonisolated global optimal solution, and it turns out that such an optimal solution is adequately guaranteed to be feasible and to be close to the actual optimal solution. It can be shown by the numerical results that the proposed algorithm is effective and the computational results can be gained in short time.