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Variational Analysis of Marginal Functions with Applications to Bilevel Programming

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Abstract

This paper pursues a twofold goal. First goal is to derive new results on generalized differentiation in variational analysis focusing mainly on a broad class of intrinsically nondifferentiable marginal/value functions. Then the results established in this direction are applied to deriving necessary optimality conditions for the optimistic version of bilevel programs, which occupy a remarkable place in optimization theory and its various applications. We obtain new sets of optimality conditions in both smooth and nonsmooth settings of finite-dimensional and infinite-dimensional spaces.

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Authors and Affiliations

  1. Department of Mathematics, Wayne State University, Detroit, MI 48202, USA

    Boris S. Mordukhovich & Hung M. Phan

  2. Department of Mathematics, University of Texas-Pan American, Edinburg, TX 78539, USA

    Nguyen Mau Nam

Authors
  1. Boris S. Mordukhovich
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  2. Nguyen Mau Nam
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  3. Hung M. Phan
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Correspondence to Boris S. Mordukhovich.

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Mordukhovich, B.S., Nam, N.M. & Phan, H.M. Variational Analysis of Marginal Functions with Applications to Bilevel Programming. J Optim Theory Appl 152, 557–586 (2012). https://doi.org/10.1007/s10957-011-9940-1

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  • DOI: https://doi.org/10.1007/s10957-011-9940-1

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