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A Unified Characterization of Nonlinear Scalarizing Functionals in Optimization

Ernest Quintana (ernest.quintana***at***mathematik.uni-halle.de)
Christiane Tammer (christiane.tammer***at***mathematik.uni-halle.de )
Gemayqzel Bouza (gema***at***matcom.uh.cu)

Abstract: Over the years, several classes of scalarization techniques in optimization have been introduced and employed in deriving separation theorems, optimality conditions and algorithms. In this paper, we study the relationships between some of those classes in the sense of inclusion. We focus on three types of scalarizing functionals (by Hiriart-Urruty, Drummond and Svaiter, Gerstewitz) and completely determine their relationships. In particular, it is shown that the class of the functionals by Gerstewitz is minimal in this sense. Furthermore, we de fine a new (and larger) class of scalarizing functionals that are not necessarily convex, but rather quasidifferentiable and positively homogeneous. We show that our results are connected with certain set relations in set optimization.

Keywords: scalarization, vector optimization, quasidifferentiability, separation theorem, dual spaces

Category 1: Convex and Nonsmooth Optimization

Category 2: Nonlinear Optimization

Category 3: Global Optimization


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Entry Submitted: 07/03/2018
Entry Accepted: 07/03/2018
Entry Last Modified: 08/02/2019

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