DigitalCommons@WayneState

Title

Variational Analysis of Marginal Functions with Applications to Bilevel Programming

Authors

Boris S. Mordukhovich, Wayne State UniversityFollow
Nguyen Mau Nam, The University of Texas-Pan American, Edinburg, TXFollow
Hung M. Phan, Wayne State UniversityFollow

Document Type

Technical Report

Abstract

This paper pursues a twofold goal. First 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 apply to deriving necessary optimality conditions for the optimistic version of bilevel programs that occupy a remarkable place in optimization theory and its various applications. We obtain new sets of optimality conditions in both smooth and smooth settings of finite-dimensional and infinite-dimensional spaces.

Number in Series

2011.10

Disciplines

Applied Mathematics | Mathematics

AMS Subject Classification

Primary 49J52, 49J53; Secondary 90C30

Comments

This research was partially supported by the US National Science Foundation under grant DMS-1007132, by the Australian Research Council under grant DP-12092508, by the Portuguese Foundation of Science and Technologies under grant MAT/11109, and by the Simons Foundation under grant #208785.

Recommended Citation

Mordukhovich, Boris S.; Nam, Nguyen Mau; and Phan, Hung M., "Variational Analysis of Marginal Functions with Applications to Bilevel Programming" (2011). Mathematics Research Reports. 91.
https://digitalcommons.wayne.edu/math_reports/91