This article is cited in 1 paper

Convergence of hausdorff approximation methods for the Edgeworth–Pareto hull of a compact set

R. V. Efremov

Universidad Rey Juan Carlos, Móstoles, Madrid, 28933, Spain

Abstract: The Hausdorff methods comprise an important class of polyhedral approximation methods for convex compact bodies, since they have an optimal convergence rate and possess other useful properties. The concept of Hausdorff methods is extended to a problem arising in multicriteria optimization, namely, to the polyhedral approximation of the Edgeworth–Pareto hull (EPH) of a convex compact set. It is shown that the sequences of polyhedral sets generated by Hausdorff methods converge to the EPH to be approximated. It is shown that the Estimate Refinement method, which is most frequently used to approximate the EPH of convex compact sets, is a Hausdorff method and, hence, generates sequences of sets converging to the EPH.

Key words: multicriteria optimization, polyhedral approximation of convex bodies, Edgeworth–Pareto hull, Hausdorff methods, Estimate Refinement method.

UDC: 519.65

MSC: Primary 90C29; Secondary 52A27, 65K05

Received: 03.03.2015
Revised: 05.05.2015

DOI: 10.7868/S004446691511006X

 English version: Computational Mathematics and Mathematical Physics, 2015, 55:11, 1771–1778

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