WIAS Preprint No. 1686, (2012)

On regular coderivatives in parametric equilibria with non-unique multipliers


  • Henrion, René
    ORCID: 0000-0001-5572-7213
  • Outrata, Jiří
  • Surowiec, Thomas
    ORCID: 0000-0003-2473-4984

2010 Mathematics Subject Classification

  • 49J53 90C31 90C46


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




This paper deals with the computation of regular coderivatives of solution maps associated with a frequently arising class of generalized equations. The constraint sets are given by (not necessarily convex) inequalities, and we do not assume linear independence of gradients to active constraints. The achieved results enable us to state several versions of sharp necessary optimality conditions in optimization problems with equilibria governed by such generalized equations. The advantages are illustrated by means of examples.

Appeared in

  • Math. Program., 136 (2012) pp. 111--131.

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