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Some remarks on stability of generalized equations

Rene Henrion (henrion***at***wias-berlin.de)
Alexander Y. Kruger (a.kruger***at***ballarat.edu.au)
Jirı V. Outrata (outrata***at***utia.cas.cz)

Abstract: The paper concerns the computation of the graphical derivative and the regular (Frechet) coderivative of the solution map to a class of generalized equations, where the multi-valued term amounts to the regular normal cone to a (possibly nonconvex) set given by C2 inequalities. Instead of the Linear Independence qualification condition, standardly used in this context, one assumes a combination of the Mangasarian-Fromovitz and the Constant Rank qualification conditions. On the basis of the obtained generalized derivatives, new optimality conditions for a class of mathematical programs with equilibrium constrains are derived, and a workable characterization of the isolated calmness of the considered solution map is provided.

Keywords: Parameterized generalized equation, regular and limiting coderivative, constant rank CQ, mathematical program with equilibrium constraint

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: Published in Journal of Optimization Theory and Applications (2013) 159 (3):681–697 DOI 10.1007/s10957-012-0147-x

Download: [Postscript][PDF]

Entry Submitted: 12/23/2011
Entry Accepted: 12/24/2011
Entry Last Modified: 01/01/2014

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