A Single-Variable Method for Solving the Min–Max Programming Problem with Addition–Overlap Function Composition

Yan-Kuen Wu, Sy-Ming Guu and Ya-Chan Chang ()
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Yan-Kuen Wu: Shaoxing Key Laboratory for Smart Society Monitoring, Prevention & Control, School of International Business, Zhejiang Yuexiu University, Shaoxing 312069, China
Sy-Ming Guu: Graduate Institute of Business and Management, College of Management, Chang Gung University, Taoyuan 33302, Taiwan
Ya-Chan Chang: Graduate Institute of Business and Management, College of Management, Chang Gung University, Taoyuan 33302, Taiwan

Mathematics, 2024, vol. 12, issue 20, 1-16

Abstract: Min–max programming problems with addition–min constraints have been studied in the literature to model data transfer in BitTorrent-like peer-to-peer file-sharing systems. It is well known that the class of overlap functions contains various operators, including the “min” operator. The aim of this paper is to generalize the above min–max programming problem with addition–overlap function constraints. We demonstrate that this new optimization problem can be transformed into a simplified single-variable optimization problem, which makes it easier to find an optimal solution. The bisection method will be used to find this optimal solution. In addition, when the overlap function is explicitly specified, an iterative method is given to compute the optimal objective value with a polynomial time complexity. A numerical example is provided to illustrate the procedures.

Keywords: min–max programming problem; single-variable method; addition–overlap function composition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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