Output-Space Branch-and-Bound Reduction Algorithm for a Class of Linear Multiplicative Programs

Bo Zhang, Yuelin Gao, Xia Liu and Xiaoli Huang
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Bo Zhang: School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China
Yuelin Gao: Ningxia Province Cooperative Innovation Center of Scientific Computing and Intelligent Information Processing, North Minzu University, Yinchuan 750021, China
Xia Liu: School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China
Xiaoli Huang: Ningxia Province Cooperative Innovation Center of Scientific Computing and Intelligent Information Processing, North Minzu University, Yinchuan 750021, China

Mathematics, 2020, vol. 8, issue 3, 1-34

Abstract: In this paper, a new relaxation bounding method is proposed for a class of linear multiplicative programs. Although the 2 p − 1 variable is introduced in the construction of equivalence problem, the branch process of the algorithm is only carried out in p − dimensional space. In addition, a super-rectangular reduction technique is also given to greatly improve the convergence rate. Furthermore, we construct an output-space branch-and-bound reduction algorithm based on solving a series of linear programming sub-problems, and prove the convergence and computational complexity of the algorithm. Finally, to verify the feasibility and effectiveness of the algorithm, we carried out a series of numerical experiments and analyzed the advantages and disadvantages of the algorithm by numerical results.

Keywords: global optimization; linear multiplicative programming; branch-and-bound; output-space; linear relaxation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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