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Optimality and Duality Results for Bilevel Programming Problem Using Convexifactors

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Abstract

The paper is devoted to the applications of convexifactors to bilevel programming problem. Here we have defined ∂ ∗-convex, ∂ ∗-pseudoconvex and ∂ ∗-quasiconvex bifunctions in terms of convexifactors on the lines of Dutta and Chandra (Optimization 53:77–94, 2004) and Li and Zhang (J. Opt. Theory Appl. 131:429–452, 2006). We derive sufficient optimality conditions for the bilevel programming problem by using these functions, and we establish various duality results by associating the given problem with two dual problems, namely Wolfe type dual and Mond–Weir type dual.

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Authors and Affiliations

  1. Department of Mathematics, Miranda House, University of Delhi, Delhi, -110007, India

    S. K. Suneja

  2. Department of Mathematics, University of Delhi, Delhi, -110007, India

    B. Kohli

Authors
  1. S. K. Suneja
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  2. B. Kohli
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Correspondence to B. Kohli.

Additional information

Communicated by V.F. Dem’yanov.

The authors are grateful to the anonymous referee for useful comments and constructive suggestions, that have greatly improved the original version of the paper.

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Suneja, S.K., Kohli, B. Optimality and Duality Results for Bilevel Programming Problem Using Convexifactors. J Optim Theory Appl 150, 1–19 (2011). https://doi.org/10.1007/s10957-011-9819-1

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  • DOI: https://doi.org/10.1007/s10957-011-9819-1

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