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


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  • Yalçın Küçük


  • İlknur Atasever
  • Mahide Küçük
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    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

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    Bibliographic Info

    Article provided by Springer in its journal Journal of Global Optimization.

    Volume (Year): 54 (2012)
    Issue (Month): 4 (December)
    Pages: 813-830

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    Handle: RePEc:spr:jglopt:v:54:y:2012:i:4:p:813-830

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    Keywords: Nonconvex analysis; Nonsmooth analysis; Weak subdifferentials; Lower Lipschitz functions; Nonconvex optimization; 90C26; 90C46; 46N95; 90J56; 49J52;

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