This article is cited in 1 paper

Hausdorff methods for approximating the convex Edgeworth–Pareto hull in integer problems with monotone objectives

A. I. Pospelov<sup>ab

a</sup> Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia
^b DATADVANCE, Pokrovskii bul. 3/1B, Moscow, Russia

Abstract: Adaptive methods for the polyhedral approximation of the convex Edgeworth–Pareto hull in multiobjective monotone integer optimization problems are proposed and studied. For these methods, theoretical convergence rate estimates with respect to the number of vertices are obtained. The estimates coincide in order with those for filling and augmentation $H$-methods intended for the approximation of nonsmooth convex compact bodies.

Key words: adaptive methods, polyhedral approximation, convergence rate, multiobjective optimization, Pareto frontier, integer optimization.

UDC: 519.658

Received: 15.05.2015
Revised: 17.12.2015

DOI: 10.7868/S0044466916080147

 English version: Computational Mathematics and Mathematical Physics, 2016, 56:8, 1388–1401

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