An approximation algorithm for convex multi-objective programming problems

In multi-objective convex optimization it is necessary to compute an infinite set of nondominated points. We propose a method for approximating the nondominated set of a multi-objective nonlinear programming problem, where the objective functions and the feasible set are convex. This method is an ex...

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Veröffentlicht in:Journal of global optimization Jg. 50; H. 3; S. 397 - 416
Hauptverfasser: Ehrgott, Matthias, Shao, Lizhen, Schöbel, Anita
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Boston Springer US 01.07.2011
Springer Nature B.V
Schlagworte:
Algorithms
Approximation
Computer Science
Convex analysis
Linear programming
Mathematics
Mathematics and Statistics
Methods
Nonlinear programming
Objectives
Operations Research/Decision Theory
Optimization
Real Functions
Studies
nondominated point
Multi-objective optimization
Approximation algorithm
Convex optimization
ISSN:0925-5001, 1573-2916
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Zusammenfassung:In multi-objective convex optimization it is necessary to compute an infinite set of nondominated points. We propose a method for approximating the nondominated set of a multi-objective nonlinear programming problem, where the objective functions and the feasible set are convex. This method is an extension of Benson’s outer approximation algorithm for multi-objective linear programming problems. We prove that this method provides a set of weakly ε -nondominated points. For the case that the objectives and constraints are differentiable, we describe an efficient way to carry out the main step of the algorithm, the construction of a hyperplane separating an exterior point from the feasible set in objective space. We provide examples that show that this cannot always be done in the same way in the case of non-differentiable objectives or constraints.
Bibliographie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-010-9588-7