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

Bo Zhang (), Hongyu Wang () and Yuelin Gao ()
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Bo Zhang: North Minzu University
Hongyu Wang: Ningxia University
Yuelin Gao: North Minzu University

Journal of Optimization Theory and Applications, 2024, vol. 202, issue 3, No 1, 997-1026

Abstract: Abstract In this study, we investigate a class of linear multiplicative programs with positive exponents. By introducing p additional variables, the original problem is reformulated into an equivalent problem (EP) within the output space. Subsequently, a novel global optimization algorithm is introduced to tackle EP. The algorithm primarily leverages two key techniques. One is the outer approximation technique, which tightens the relaxed feasible region of EP and improves the upper bound by carefully examining suitable feasible points. The other is the branch and bound technique to guarantee the global optimality of the solution. Numerical results confirm the effectiveness and practicality of the proposed algorithm, thereby underscoring its potential for real-world applications.

Keywords: Global optimization; Linear multiplicative program; Branch-and-bound; Outer approximation; 90C26; 90C30 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02461-y

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