Conditioning for optimization problems under general perturbations

Monica Bianchi, Rita Pini, G. Kassay, R. Pini

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

Given a function f in the class C^(1,1)B(0, r), where B(0, r) denotes a ball of radius r in a real Banach space E, we provide the definition of a positive extended real number c*(f ) defined through the function, that plays a role in the study of the sensitivity of the Argmin map of the perturbed function F_g (p, u) = f (u) − g(p, u). This number coincides with the number c_2(f ) introduced by Zolezzi (2003) if linear perturbations g(p, u) = <p, u> are considered.
Original languageEnglish
Pages (from-to)37-45
Number of pages9
JournalNONLINEAR ANALYSIS
Volume2012
DOIs
Publication statusPublished - 2012

Keywords

  • condition number theory
  • convex optimization
  • sensitivity

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