Image space branch-reduction-bound algorithm for globally minimizing a class of multiplicative problems

¹ School of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang 453003, China
² School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, P.R. China

^* Corresponding author: jiaohongwei@126.com

Received: 22 November 2021
Accepted: 1 May 2022

Abstract

This paper presents an image space branch-reduction-bound algorithm for solving a class of multiplicative problems (MP). First of all, by introducing auxiliary variables and taking the logarithm of the objective function, an equivalent problem (EP) of the problem (MP) is obtained. Next, by using a new linear relaxation technique, the parametric linear relaxation programming (PLRP) of the equivalence problem (EP) can be established for acquiring the lower bound of the optimal value to the problem (EP). Based on the characteristics of the objective function of the equivalent problem and the structure of the branch-and-bound algorithm, some region reduction techniques are constructed for improving the convergence speed of the algorithm. Finally, the global convergence of the algorithm is proved and its computational complexity is estimated, and numerical experiments are reported to indicate the higher computational performance of the algorithm.