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In the paper, some problems of vector optimization are considered. Vector optimality is understood in the Pareto sense. Using the notion of Ponstein convexity, we formulate a 'scalarization' theorem. Two examples (vector optimization in IR^2 and an optimal-control problem for a parabolic equation with a vector performance index) are discussed. A Pareto boundary and a Salukwadze optimum are obtained for each of them. Additionally, for some vector optimization problems in IR^2, a criterion space is found. All calculations are performed with the use of Maple V. In the Appendix, a sketch of the proof of the main theorem on 'scalarization' is given.
Rocznik
Tom
Strony
465--485
Opis fizyczny
Bibliogr. 14 poz., wykr.
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autor
- Institute of Informatics, Silesian University ul. Bedzinska 60, 41?200 Sosnowiec, Poland, kotarski@gate.math.us.edu.pl
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bwmeta1.element.baztech-article-BPZ1-0014-0026