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Necessary optimality conditions in pessimistic bilevel programming

Stephan Dempe(dempe***at***tu-freiberg.de)
Boris S. Mordukhovich(boris***at***math.wayne.edu)
Alain B. Zemkoho(zemkoho***at***student.tu-freiberg.de)

Abstract: This paper is devoted to the so-called pessimistic version of bilevel programming programs. Minimization problems of this type are challenging to handle partly because the corresponding value functions are often merely upper (while not lower) semicontinuous. Employing advanced tools of variational analysis and generalized differentiation, we provide rather general frameworks ensuring the Lipschitz continuity of the corresponding value functions. Several types of lower subdi fferential necessary optimality conditions are then derived by using the lower-level value function (LLVF) approach and the Karush-Kuhn-Tucker (KKT) representation of lower-level optimal solution maps. We also derive upper subdiff erential necessary optimality conditions of a new type, which can be essentially stronger than the lower ones in some particular settings. Finally, certain links are established between the obtained necessary optimality conditions for the pessimistic and optimistic versions in bilevel programming.

Keywords: optimization and variational analysis; pessimistic bilevel programs; two-level value functions; sensitivity analysis; generalized diff erentiation; optimality conditions

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: TU Bergakademie Freiberg, Fakultaet fuer Mathematik und Informatik, Preprint 2012-01

Download: [PDF]

Entry Submitted: 01/10/2012
Entry Accepted: 01/10/2012
Entry Last Modified: 01/10/2012

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