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

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

JOURNAL OF GLOBAL OPTIMIZATION, cilt.54, sa.4, ss.813-830, 2012 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 54 Sayı: 4
  • Basım Tarihi: 2012
  • Doi Numarası: 10.1007/s10898-011-9794-y
  • Dergi Adı: JOURNAL OF GLOBAL OPTIMIZATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.813-830
  • Anahtar Kelimeler: Nonconvex analysis, Nonsmooth analysis, Weak subdifferentials, Lower Lipschitz functions, Nonconvex optimization, EXTENSION
  • Anadolu Üniversitesi Adresli: Evet

Özet

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.