Weak subdifferential/superdifferential, weak exhausters and optimality conditions

KÜÇÜK M., Urbański R., Grzybowski J., Küçük Y., Atasever Güvenç İ., Tozkan D., ...More

Optimization, vol.64, no.10, pp.2199-2212, 2015 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 64 Issue: 10
  • Publication Date: 2015
  • Doi Number: 10.1080/02331934.2014.929682
  • Journal Name: Optimization
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2199-2212
  • Keywords: exhausters, optimality conditions, weak exhausters, weak subdifferential, weak superdifferential
  • Uşak University Affiliated: Yes

Abstract

In this work, the notion of weak superdifferential is presented. Some calculation rules are given to evaluate weak subdifferential and weak superdifferential of some classes of functions represented by support functions. Moreover, some methods are obtained to calculate weak subdifferential of convex functions. In addition, the concept of weak lower and weak upper exhausters of positively homogeneous functions are introduced by using weak subdifferential and weak superdifferential, respectively. In terms of weak exhausters, some optimality conditions are given to find local or global minimizers/maximizers of some classes of functions.