Some results on condition numbers in convex multiobjective optimization

Monica Bianchi, Enrico Miglierina, Rita Pini, Elena Molho

Research output: Working paper

Abstract

Abstract Various notions of condition numbers are used to study some sensitivity aspects of scalar optimization problems. The aim of this paper is to introduce a notion of condition number to treat the case of a multiobjective optimization problem defined via m convex C^{1,1} objective functions on a given closed ball in \mathbb{R}^{n}. Two approaches are proposed: the first one adopts a local point of view around a solution point, whereas the second one considers the solution set as a whole. We underline that, in the scalar case, both of them reduce to the condition number proposed by Zolezzi. Extensions of the Eckart--Young distance theorem are proved in both cases.
Original languageEnglish
Number of pages16
Publication statusPublished - 2011

Keywords

  • Condition Number
  • Eckart-Young theorem
  • sensitivity in multiobjective optimization

Fingerprint

Dive into the research topics of 'Some results on condition numbers in convex multiobjective optimization'. Together they form a unique fingerprint.

Cite this