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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

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

Suggested Citation

  • Yalçın Küçük & İlknur Atasever & Mahide Küçük, 2012. "Weak Fenchel and weak Fenchel-Lagrange conjugate duality for nonconvex scalar optimization problems," Journal of Global Optimization, Springer, vol. 54(4), pages 813-830, December.
    • Handle: RePEc:spr:jglopt:v:54:y:2012:i:4:p:813-830
    DOI: 10.1007/s10898-011-9794-y
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    References listed on IDEAS

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    1. R. I. Boţ & G. Kassay & G. Wanka, 2005. "Strong Duality for Generalized Convex Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 127(1), pages 45-70, October.
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