Reduction of Weak Exhausters and Optimality Conditions via Reduced Weak Exhausters

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

Journal of Optimization Theory and Applications, vol.165, no.3, pp.693-707, 2015 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 165 Issue: 3
  • Publication Date: 2015
  • Doi Number: 10.1007/s10957-014-0592-9
  • Journal Name: Journal of Optimization Theory and Applications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.693-707
  • Keywords: Exhausters, Optimality conditions, Reduced weak exhausters, Weak exhausters, Weak subdifferential
  • Uşak University Affiliated: Yes

Abstract

In this work, it is proved that weak exhausters of a positively homogeneous function can be reduced if weak subdifferential/superdifferential can be represented as the sum of a subset of it and weak subdifferential of zero function. It is also shown that weak exhausters can be reduced if this subset is the set of minimal elements of weak subdifferential/superdifferential with respect to weak subdifferential of zero function. At the end, some optimality conditions are given using reduced weak exhausters.