International Journal of applied mathematics and computer science

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Paper details

Number 3 - September 2000
Volume 10 - 2000

On Pareto and Salukwadze optimization problems

Wiesław Kotarski

Abstract
n 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 R2 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 R2, 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.

Keywords
Pareto and Salukwadze optima, Pareto boundary, criterion space, scalarizarion