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An efficient interior-point method for convex multicriteria optimization problems

An efficient interior-point method for convex multicriteria optimization problems
An efficient interior-point method for convex multicriteria optimization problems
In multicriteria optimization, several objective functions have to be minimized simultaneously. We propose a new efficient method for approximating the solution set of a multicriteria optimization problem, where the objective functions involved are arbitrary convex functions and the set of feasible points is convex. The method is based on generating warm-start points for an efficient interior-point algorithm, while the approximation computed consists of a finite set of discrete points. Polynomial-time complexity results for the method proposed are derived. In these estimates, the number of operations per point decreases when the number of points generated for the approximation increases. This reduced theoretical complexity estimate is a novel feature and is not observed in standard solution techniques for multicriteria optimization problems.
convex multicriteria optimization, interior point, polynomial time
0364-765X
825-845
Fliege, Jörg
54978787-a271-4f70-8494-3c701c893d98
Fliege, Jörg
54978787-a271-4f70-8494-3c701c893d98

Fliege, Jörg (2006) An efficient interior-point method for convex multicriteria optimization problems. Mathematics of Operations Research, 31 (4), 825-845. (doi:10.1287/moor.1060.0221).

Record type: Article

Abstract

In multicriteria optimization, several objective functions have to be minimized simultaneously. We propose a new efficient method for approximating the solution set of a multicriteria optimization problem, where the objective functions involved are arbitrary convex functions and the set of feasible points is convex. The method is based on generating warm-start points for an efficient interior-point algorithm, while the approximation computed consists of a finite set of discrete points. Polynomial-time complexity results for the method proposed are derived. In these estimates, the number of operations per point decreases when the number of points generated for the approximation increases. This reduced theoretical complexity estimate is a novel feature and is not observed in standard solution techniques for multicriteria optimization problems.

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More information

Published date: November 2006
Keywords: convex multicriteria optimization, interior point, polynomial time
Organisations: Operational Research

Identifiers

Local EPrints ID: 48858
URI: http://eprints.soton.ac.uk/id/eprint/48858
ISSN: 0364-765X
PURE UUID: ec902ced-e061-4d88-ab4b-be395edc9ce2
ORCID for Jörg Fliege: ORCID iD orcid.org/0000-0002-4459-5419

Catalogue record

Date deposited: 16 Oct 2007
Last modified: 17 Dec 2019 01:43

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