Global algorithm for solving linear multiplicative programming problems
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This article presents a rectangular branch-and-bound algorithm with standard bisection rule for solving linear multiplicative problem (LMP). In this algorithm, a novel linear relaxation technique is presented for deriving the linear relaxation programming of problem LMP, which has separable characteristics and can be used to acquire the upper bound of the optimal value to problem LMP. Thus, to obtain a global optimal solution for problem LMP, the main computational work of the algorithm involves the solutions of a sequence of linear programming problems. Moreover, the proof of its convergence property and the numerical result show the feasibility and efficiency of the presented algorithm.
KeywordsGlobal optimization Branch-and-bound Linear multiplicative programming
The authors are grateful to the responsible editor and the anonymous referees for their valuable comments and suggestions, which have greatly improved the earlier version of this paper. This paper is supported by National Natural Science Foundation of China (11671122, 11871196, 11171094), and by the Key Scientific Research Project for Universities in Henan Province (17A110006).
- 20.Yang, L.P., Shen, P.P., Pei, Y.G.: A global optimization approach for solving generalized nonlinear multiplicative programming problem. Abstr. Appl. Anal. (2014). https://doi.org/10.1155/2014/641909