The aim of this work is to characterize the various sets of solutions of a vector optimization problem by means of a unique special scalarizing function. The different efficient frontiers are found as optimal scalar solutions according to a more restrictive definition of minimality: strict minima, sharp minima, well-posed minima. Moreover we link the notion of proper efficiency to some sort of stability of the scalar problem. In order to this goal, we study the convergence of the solutions of a suitable family of perturbed problems using the Kuratowski set-convergence.
Miglierina, E., Molho, E., Zaffaroni, A., Different solutions in Vector Optimization: a Characterization by a special scalarization, in Optimization in Economics, Finance and Industry, (Verona, 14-15 June 2001), datanova, Milano 2002:- 185-198 [http://hdl.handle.net/10807/1454]
Different solutions in Vector Optimization: a Characterization by a special scalarization
Miglierina, Enrico;
2002
Abstract
The aim of this work is to characterize the various sets of solutions of a vector optimization problem by means of a unique special scalarizing function. The different efficient frontiers are found as optimal scalar solutions according to a more restrictive definition of minimality: strict minima, sharp minima, well-posed minima. Moreover we link the notion of proper efficiency to some sort of stability of the scalar problem. In order to this goal, we study the convergence of the solutions of a suitable family of perturbed problems using the Kuratowski set-convergence.
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