WIAS Preprint No. 1678, (2012)

Some remarks on stability of generalized equations



Authors

  • Henrion, René
  • Kruger, Alexander
  • Outrata, Jiří

2010 Mathematics Subject Classification

  • 49J53 90C31 90C46

Keywords

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

DOI

10.20347/WIAS.PREPRINT.1678

Abstract

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 multi-valued term amounts to the regular normal cone to a (possibly nonconvex) set given by $C^2$ 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.

Appeared in

  • J. Optim. Theory Appl., 159 (2013) pp. 681--697.

Download Documents