A Single-Variable Method for Solving the Min–Max Programming Problem with Addition–Overlap Function Composition
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 p...
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Published in | Mathematics (Basel) Vol. 12; no. 20; p. 3183 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
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01.10.2024
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ISSN | 2227-7390 2227-7390 |
DOI | 10.3390/math12203183 |
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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. |
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AbstractList | 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. |
Audience | Academic |
Author | Chang, Ya-Chan Wu, Yan-Kuen Guu, Sy-Ming |
Author_xml | – sequence: 1 givenname: Yan-Kuen orcidid: 0000-0001-7788-8157 surname: Wu fullname: Wu, Yan-Kuen – sequence: 2 givenname: Sy-Ming surname: Guu fullname: Guu, Sy-Ming – sequence: 3 givenname: Ya-Chan surname: Chang fullname: Chang, Ya-Chan |
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SubjectTerms | addition–overlap function composition Computer programming Constraints Data transfer (computers) File sharing Iterative methods Linear programming Maxima and minima min–max programming problem Norms Operators (mathematics) Optimization Peer to peer computing Polynomials Preferences Programming single-variable method Tests, problems and exercises Variables Variables (Mathematics) |
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Title | A Single-Variable Method for Solving the Min–Max Programming Problem with Addition–Overlap Function Composition |
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