A vector linear programming approach for certain global optimization problems

Global optimization problems with a quasi-concave objective function and linear constraints are studied. We point out that various other classes of global optimization problems can be expressed in this way. We present two algorithms, which can be seen as slight modifications of Benson-type algorithm...

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Veröffentlicht in:Journal of global optimization Jg. 72; H. 2; S. 347 - 372
Hauptverfasser: Ciripoi, Daniel, Löhne, Andreas, Weißing, Benjamin
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.10.2018
Springer
Springer Nature B.V
Schlagworte:
Algorithms
Computer Science
Global optimization
Linear programming
Mathematics
Mathematics and Statistics
Multiple objective analysis
Nonlinear programming
Operations Research/Decision Theory
Optimization
Real Functions
Global optimization
52B55
DC programming
90C29
Linear vector optimization
90C26
Multiobjective linear programming
ISSN:0925-5001, 1573-2916
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Zusammenfassung:Global optimization problems with a quasi-concave objective function and linear constraints are studied. We point out that various other classes of global optimization problems can be expressed in this way. We present two algorithms, which can be seen as slight modifications of Benson-type algorithms for multiple objective linear programs (MOLP). The modification of the MOLP algorithms results in a more efficient treatment of the studied optimization problems. This paper generalizes results of Schulz and Mittal (Math Program 141(1–2):103–120, 2013 ) on quasi-concave problems and Shao and Ehrgott (Optimization 65(2):415–431, 2016 ) on multiplicative linear programs. Furthermore, it improves results of Löhne and Wagner (J Glob Optim 69(2):369–385, 2017 ) on minimizing the difference f = g - h of two convex functions g , h where either g or h is polyhedral. Numerical examples are given and the results are compared with the global optimization software BARON.
Bibliographie:ObjectType-Article-1
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-018-0627-0