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

Yalçın Küçük (), İlknur Atasever and Mahide Küçük

Journal of Global Optimization, 2012, vol. 54, issue 4, 813-830

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, $${(D_F^w)}$$ , and weak Fenchel Lagrange conjugate dual problem $${(D_{FL}^w)}$$ are constructed. Necessary and sufficient conditions for strong duality for the $${(D_F^w)}$$ , $${(D_{FL}^w)}$$ 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 ), $${(D_F^w)}$$ , $${(D_{FL}^w)}$$ dual problems and primal problem are examined. Lastly, necessary and sufficient optimality conditions for the primal and the dual problems $${(D_F^w)}$$ and $${(D_{FL}^w)}$$ are established. Copyright Springer Science+Business Media, LLC. 2012

Keywords: Nonconvex analysis; Nonsmooth analysis; Weak subdifferentials; Lower Lipschitz functions; Nonconvex optimization; 90C26; 90C46; 46N95; 90J56; 49J52 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10898-011-9794-y

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