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An Efficient Interior-Point Method for Convex Multicriteria Optimization Problems

Joerg Fliege (fliege***at***math.uni-dortmund.de)

Abstract: In multicriteria optimization, several objective functions, conflicting with each other, have to be minimized simultaneously. We propose a new efficient method for approximating the solution set of a multiobjective programming problem, where the objective functions involved are arbitary 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. Complexity results for the method proposed are derived. It turns out that the number of operations per point \emph{decreases} when the number of points generated for the approximation \emph{increases}.

Keywords: multicriteria, vector optimization, interior-point, selfconcordant, warm-start

Category 1: Other Topics (Multi-Criteria Optimization )

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )

Citation: Ergebnisberichte Angewandte Mathematik, Nr.~248. Fachbereich Mathematik, Universit{\

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Entry Submitted: 03/09/2004
Entry Accepted: 03/19/2004
Entry Last Modified: 03/09/2004

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