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Zh. Vychisl. Mat. Mat. Fiz., 2015, Volume 55, Number 10, Pages 1681–1693 (Mi zvmmf10282)  

This article is cited in 3 scientific papers (total in 3 papers)

Decomposition of the problem of approximating the Edgeworth–Pareto hull

A. V. Lotov

Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia

Abstract: For nonlinear block separable multicriteria optimization (MCO) problems, a decomposition method is proposed that simplifies the approximation of the Edgeworth–Pareto hull (EPH), i.e., the maximum (by inclusion) set having the same Pareto frontier as the set of feasible criteria vectors in the MCO problem. A two-level system is considered that consists of an upper coordinating level and lower-level subsystems interacting via the upper level. It is assumed that the criteria are related to the upper-level variables. According to the method, preliminarily constructed approximations to block EPHs are used to obtain an EPH approximation for the whole MCO problem. As an example, the EPH for an MCO problem arising in estimating the potential possibilities of water resource management for a cascade of reservoirs is constructed.

Key words: nonlinear multicriteria optimization, Edgeworth–Pareto hull, approximation, block separable structure.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-11-00432


DOI: https://doi.org/10.7868/S0044466915100166

Full text: PDF file (322 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2015, 55:10, 1653–1664

Bibliographic databases:

UDC: 519.642.8
Received: 12.03.2015

Citation: A. V. Lotov, “Decomposition of the problem of approximating the Edgeworth–Pareto hull”, Zh. Vychisl. Mat. Mat. Fiz., 55:10 (2015), 1681–1693; Comput. Math. Math. Phys., 55:10 (2015), 1653–1664

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. M. V. Bolgov, A. L. Buber, A. A. Komarovskii, A. V. Lotov, “Searching for compromise solution in the planning and managing of releases into the lower pool of the Volgograd hydropower system 1. Strategic planning”, Water Resour., 45:5 (2018), 819–826  crossref  isi  scopus
    2. I. Kaliszewski, J. Miroforidis, “On upper approximations of Pareto fronts”, J. Glob. Optim., 72:3 (2018), 475–490  crossref  mathscinet  isi  scopus
    3. M. V. Bolgov, A. L. Buber, A. V. Lotov, “Support for making strategic decisions on the water supply of the lower Volga River based on the Pareto frontier visualization”, Sci. Tech. Inf. Process., 45:5 (2018), 297–306  crossref  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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