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Pareto-optimality conditions in discrete vector optimization problems

Pareto-optimality conditions in discrete vector optimization problems -- For the vector optimization problem /(*)-> min V i Nn = {1,2,...,«}, with a finite set of vector estimators F(X) we give a wide class of efficiency (Pareto-optimality) criteria in terms of linear convolutions of transformed partial criteria. In particular, it is proved that an element x° e X is efficient if and only if there exists a vector (, ,..., ,,), , > , i , such that VJCG X, ieN,, ieN,, where = «1/, = min{//(jc) -.//(*') > 0: :,/ e , i e N,,}. This research was supported by the Foundation for Basic Research of Republic Byelarus (grants F95-70 and MP96-35), and the DAAD and the International Soros Educational Program in Exact Sciences (grant 'Soros Professor' for the first of the authors). For the vector multicriteria optimization problems, there are many necessary and sufficient conditions for the solution to be optimal in some sense. This is motivated by the circumstance that most of the methods to solve these problems are based on the optimality (efficiency) conditions, which, as a rule, establish a connection between the optimal alternatives of the vector problem and the optimal solutions of the one-dimensional parametric problem with an aggregated (generalized) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Discrete Mathematics and Applications de Gruyter

Pareto-optimality conditions in discrete vector optimization problems

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Publisher
de Gruyter
Copyright
Copyright © 2009 Walter de Gruyter
ISSN
0924-9265
eISSN
1569-3929
DOI
10.1515/dma.1997.7.4.345
Publisher site
See Article on Publisher Site

Abstract

-- For the vector optimization problem /(*)-> min V i Nn = {1,2,...,«}, with a finite set of vector estimators F(X) we give a wide class of efficiency (Pareto-optimality) criteria in terms of linear convolutions of transformed partial criteria. In particular, it is proved that an element x° e X is efficient if and only if there exists a vector (, ,..., ,,), , > , i , such that VJCG X, ieN,, ieN,, where = «1/, = min{//(jc) -.//(*') > 0: :,/ e , i e N,,}. This research was supported by the Foundation for Basic Research of Republic Byelarus (grants F95-70 and MP96-35), and the DAAD and the International Soros Educational Program in Exact Sciences (grant 'Soros Professor' for the first of the authors). For the vector multicriteria optimization problems, there are many necessary and sufficient conditions for the solution to be optimal in some sense. This is motivated by the circumstance that most of the methods to solve these problems are based on the optimality (efficiency) conditions, which, as a rule, establish a connection between the optimal alternatives of the vector problem and the optimal solutions of the one-dimensional parametric problem with an aggregated (generalized)

Journal

Discrete Mathematics and Applications – de Gruyter

Published: Jan 1, 1997

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