Variational Analysis of Marginal Functions with Applications to Bilevel Programming

Variational Analysis of Marginal Functions with Applications to Bilevel Programming

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Article ID: iaor2012629
Volume: 152
Issue: 3
Start Page Number: 557
End Page Number: 586
Publication Date: Mar 2012
Journal: Journal of Optimization Theory and Applications
Authors: , ,
Keywords: programming (bilevel)
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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