Geodesic
On Pareto and Salukwadze Optimization Problems
International Journal of Applied Mathematics and Computer Science, Tome 10 (2000) no. 3, pp. 465-485

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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.
Keywords: Pareto and Salukwadze optima, Pareto boundary, criterion space, scalarization
Mots-clés : brzeg Pareto, optymalizacja 
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     author = {Kotarski, W.},
     title = {On {Pareto} and {Salukwadze} {Optimization} {Problems}},
     journal = {International Journal of Applied Mathematics and Computer Science},
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Kotarski, W. On Pareto and Salukwadze Optimization Problems. International Journal of Applied Mathematics and Computer Science, Tome 10 (2000) no. 3, pp. 465-485. http://geodesic.mathdoc.fr/item/IJAMCS_2000_10_3_a1/