Variational Analysis of Marginal Functions with Applications to Bilevel Programming

Boris S. Mordukhovich (), Nguyen Mau Nam () and Hung M. Phan ()
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Boris S. Mordukhovich: Wayne State University
Nguyen Mau Nam: University of Texas-Pan American
Hung M. Phan: Wayne State University

Journal of Optimization Theory and Applications, 2012, vol. 152, issue 3, No 1, 557-586

Abstract: 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.

Keywords: Variational analysis and optimization; Bilevel programming; Generalized differentiation; Marginal functions; Optimality conditions (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-011-9940-1

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