Weak Fenchel and weak Fenchel-Lagrange conjugate duality for nonconvex scalar optimization problems

KÜÇÜK Y., ATASEVER GÜVENÇ İ., Kucuk M.

JOURNAL OF GLOBAL OPTIMIZATION, vol.54, no.4, pp.813-830, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 54 Issue: 4
  • Publication Date: 2012
  • Doi Number: 10.1007/s10898-011-9794-y
  • Journal Name: JOURNAL OF GLOBAL OPTIMIZATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.813-830
  • Keywords: Nonconvex analysis, Nonsmooth analysis, Weak subdifferentials, Lower Lipschitz functions, Nonconvex optimization, EXTENSION
  • Anadolu University Affiliated: Yes

Abstract

In this work, by using weak conjugate maps given in (Azimov and Gasimov, in Int J Appl Math 1:171-192, 1999), weak Fenchel conjugate dual problem, , and weak Fenchel Lagrange conjugate dual problem are constructed. Necessary and sufficient conditions for strong duality for the , and primal problem are given. Furthermore, relations among the optimal objective values of dual problem constructed by using Augmented Lagrangian in (Azimov and Gasimov, in Int J Appl Math 1:171-192, 1999), , dual problems and primal problem are examined. Lastly, necessary and sufficient optimality conditions for the primal and the dual problems and are established.