Outer space branch and bound algorithm for solving linear multiplicative programming problems

Peiping Shen (), Kaimin Wang and Ting Lu
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Peiping Shen: North China University of Water Resources and Electric Power
Kaimin Wang: Henan Normal University
Ting Lu: Henan Normal University

Journal of Global Optimization, 2020, vol. 78, issue 3, No 3, 453-482

Abstract: Abstract In this paper, we consider a linear multiplicative programming problem (LMP) that is known to be NP-hard even with one product term. We first introduce the auxiliary variables to obtain an equivalent problem of problem LMP. An outer space branch and bound algorithm is then designed, which integrates some basic operations such as the linear relaxation technique, branching rule and region reduction technique. The global convergence of the proposed algorithm is established by means of the subsequent solutions of a series of linear programming problems, and its computational complexity is estimated on the basis of the branching rule. Also, we discuss the relationship between the proposed linear relaxation and existing relaxations for LMP. Finally, preliminary numerical results demonstrate the proposed algorithm can efficiently find the globally optimal solutions for test instances.

Keywords: Linear multiplicative programming; Global optimization; Linear relaxation; Branch and bound; 90C30; 90C33; 90C15 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10898-020-00919-7

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