An Out Space Accelerating Algorithm for Generalized Affine Multiplicative Programs Problem

Lei Cai,Jingben Yin,Hongwei Jiao,Zhisong Hou,Shuai Tang

doi:10.1155/2017/5249160

Lei Cai, Jingben Yin + Show 3 more

Open Access

https://doi.org/10.1155/2017/5249160

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Abstract

This paper presents an out space branch-and-bound algorithm for solving generalized affine multiplicative programs problem. Firstly, by introducing new variables and constraints, we transform the original problem into an equivalent nonconvex programs problem. Secondly, by utilizing new linear relaxation technique, we establish the linear relaxation programs problem of the equivalent problem. Thirdly, based on the out space partition and the linear relaxation programs problem, we construct an out space branch-and-bound algorithm. Fourthly, to improve the computational efficiency of the algorithm, an out space reduction operation is employed as an accelerating device for deleting a large part of the investigated out space region. Finally, the global convergence of the algorithm is proved, and numerical results demonstrate the feasibility and effectiveness of the proposed algorithm.

Highlights

The generalized affine multiplicative programs problem (GAMP) arises naturally in many practical applications including management science, engineering optimization design, optimal control, Euclidean geometry, economic planning, production planning, and combinatorial mathematics [1, 2]
It is very necessary to establish an effective algorithm for globally solving the problem (GAMP)
To improve the computational efficiency of the algorithm, an out space reduction operation is employed as an accelerating device for deleting a large part of the investigated out space region

Summary

Introduction

The generalized affine multiplicative programs problem (GAMP) arises naturally in many practical applications including management science, engineering optimization design, optimal control, Euclidean geometry, economic planning, production planning, and combinatorial mathematics [1, 2]. There exist some algorithms which can be used to solve the generalized linear multiplicative programming problem, as far as we know, it is still necessary to propose a more efficient algorithm for globally solving (GAMP). Based on the out space partition and the linear relaxation programs problem, we construct an out space branch-and-bound algorithm. In this algorithm, the proposed branching operation takes place in Rp, rather than Rn or R2p; this economizes the required computation. The some concluding remarks of this paper are elaborated

Equivalent Problem and Its Linear Relaxation

Algorithm and Its Convergence

Algorithm Steps

Numerical Experiments

Concluding Remarks