WIAS Preprint No. 1678, (2012)

Some remarks on stability of generalized equations


  • Henrion, René
    ORCID: 0000-0001-5572-7213
  • Kruger, Alexander
  • Outrata, Jiří

2010 Mathematics Subject Classification

  • 49J53 90C31 90C46


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




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.

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