# On Stability of a Class of Equilibrium Problems

Jiri Outrata^{*}

We consider a class of parameterized equilibria governed by a generalized equation (GE) in which the set-valued term amounts to the normal cone to a constraint set given by (not necessarily convex) inequalities. Under various assumptions imposed on the problem data, we compute the graphical derivative and the regular and limiting coderivatives of the respective solution map and the so-called enhanced solution map which involves also the associated Lagrange multipliers. These assumptions make use apart from standard constraint qualifications like Mangasarian-Fromovitz (MFCQ) or Constant Rank also the recently developed “Relaxed” MFCQ. The computed generalized derivatives will be applied to stability analysis of the solution maps and to optimality conditions for mathematical programs with equilibrium constraints (MPECs) in which the equilibria are modeled via the considered GE.

Mathematics Subject Classification: 90C31 90C33

Keywords: Parameterized equilibrium problems; Solution maps; Generalized derivatives; Stability.

Minisymposion: Stability, Sensitivity and Error Analysis for Optimal Control Problems