A Benson-type algorithm for bounded convex vector optimization problems with vertex selection

We present an algorithm for approximately solving bounded convex vector optimization problems. The algorithm provides both an outer and an inner polyhedral approximation of the upper image. It is a modification of the primal algorithm presented by Löhne, Rudloff, and Ulus in 2014. There, vertices of...

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Bibliographic Details
Published in:Optimization methods & software Vol. 37; no. 3; pp. 1006 - 1026
Main Authors: Dörfler, Daniel, Löhne, Andreas, Schneider, Christopher, Weißing, Benjamin
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 04.05.2022
Taylor & Francis Ltd
Subjects:
90-08
Algorithms
Apexes
Approximation
convex programming
Mathematical analysis
multiple objective optimization
Optimization
polyhedral approximation
Vector optimization
ISSN:1055-6788, 1029-4937
Online Access:Get full text
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Summary:We present an algorithm for approximately solving bounded convex vector optimization problems. The algorithm provides both an outer and an inner polyhedral approximation of the upper image. It is a modification of the primal algorithm presented by Löhne, Rudloff, and Ulus in 2014. There, vertices of an already known outer approximation are successively cutoff to improve the approximation error. We propose a new and efficient selection rule for deciding which vertex to cutoff. Numerical examples are provided which illustrate that this method may solve fewer scalar problems overall and therefore may be faster while achieving the same approximation quality.
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ISSN:1055-6788
1029-4937
DOI:10.1080/10556788.2021.1880579