Scalarization of Set-Valued Optimization Problems in Normed Spaces

Enrico Miglierina, César Gutiérrez, Bienvenido Jiménez, Elena Molho

Research output: Chapter in Book/Report/Conference proceedingChapter

2 Citations (Scopus)

Abstract

This work focuses on scalarization processes for nonconvex set-valued optimization problems whose solutions are defined by the socalled l-type less order relation, the final space is normed and the ordering cone is not necessarily solid. A scalarization mapping is introduced, which generalizes the well-known oriented distance, and its main properties are stated. In particular, by choosing a suitable norm it is shown that it coincides with the generalization of the so-called Tammer-Weidner nonlinear separation mapping to this kind of optimization problems. After that, two concepts of solution are characterized in terms of solutions of associated scalar optimization problems defined through the new scalarization mapping.
Original languageEnglish
Title of host publicationModelling, Computation and Optimization in Information Systems and Management Sciences
EditorsThi Hoai An Le, Dinh Tao Pham, Ngoc Thanh Nguyen
Pages505-512
Number of pages8
Volume359
DOIs
Publication statusPublished - 2015

Publication series

NameADVANCES IN INTELLIGENT SYSTEMS AND COMPUTING

Keywords

  • L-type less order relatio
  • Minimal solution
  • Optimality conditions
  • Oriented distance
  • Scalarization
  • Set-valued optimization
  • Strict minimal solution

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