Global optimization algorithm for solving linear multiplicative programming problems

In this paper, a class of linear multiplicative problems (LMP) are considered, which cover many applications and are known to be NP-hard. For finding the globally optimal solution to problem (LMP) with a pre-specified ε-tolerance, problem (LMP) is first transformed into an equivalent problem (EP) vi...

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Bibliographic Details
Published in:Optimization Vol. 71; no. 6; pp. 1421 - 1441
Main Authors: Shen, Peiping, Wang, Kaimin, Lu, Ting
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis 03.06.2022
Taylor & Francis LLC
Subjects:
Algorithms
branch and bound
Branch and bound methods
computational complexity
Global optimization
linear multiplicative programming
linear relaxation technique
Upper bounds
ISSN:0233-1934, 1029-4945
Online Access:Get full text
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Summary:In this paper, a class of linear multiplicative problems (LMP) are considered, which cover many applications and are known to be NP-hard. For finding the globally optimal solution to problem (LMP) with a pre-specified ε-tolerance, problem (LMP) is first transformed into an equivalent problem (EP) via introducing the variable transformation. And, a novel linear relaxation technique is presented by exploiting the special structure of problem (EP), for deriving the linear relaxation programming which can be used to acquire the upper bound of the optimal value to problem (EP). A branch and bound algorithm is then located for globally solving problem (LMP). The convergence of the algorithm is established and its computational complexity is estimated. Finally, numerical results are reported to illustrate the feasibility and efficiency of the proposed algorithm.
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ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2020.1812603