Some Remarks on Stability of Generalized Equations

0392735 - ÚTIA 2014 RIV US eng J - Journal Article
Outrata, Jiří - Henrion, R. - Kruger, A.Y.
Some Remarks on Stability of Generalized Equations.
Journal of Optimization Theory and Applications. Roč. 159, č. 3 (2013), s. 681-697. ISSN 0022-3239. E-ISSN 1573-2878
R&D Projects: GA AV ČR IAA100750802; GA ČR(CZ) GAP201/12/0671
Institutional support: RVO:67985556
Keywords : Parameterized generalized equation * Regular and limiting coderivative * Constant rank CQ * Mathematical program with equilibrium constraints
Subject RIV: BA - General Mathematics
Impact factor: 1.406, year: 2013
http://library.utia.cas.cz/separaty/2013/MTR/outrata-some remarks on stability of generalized equations.pdf

The paper concerns the computation of the graphical derivative and the regular (Fréchet) coderivative of the solution map to a class of generalized equations, where the multivalued 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. Based on the obtained generalized derivatives, new optimality conditions for a class of mathematical programs with equilibrium constraints are derived, and a workable characterization of the isolated calmness of the considered solution map is provided.
Permanent Link: http://hdl.handle.net/11104/0221806