On Pareto and Salukwadze optimization problems - Kotarski, Wiesław (Zielona Góra: Uniwersytet Zielonogórski)
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 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