Convergence properties of a regularization scheme for mathematical programs with complementarity constraints. (English) Zbl 1010.90086

Summary: We study the convergence behavior of a sequence of stationary points of a parametric NLP which regularizes a mathematical program with equilibrium constraints (MPEC) in the form of complementarity conditions. Accumulation points are feasible points of the MPEC; they are C-stationary if the MPEC linear independence constraint qualification holds; they are M-stationary if, in addition, an approaching subsequence satisfies second order necessary conditions, and they are B-stationary if, in addition, an upper level strict complementarity condition holds. These results complement recent results of M. Fukushima and J.-S. Pang [Springer Lect. Notes Econ. Math. Syst. 477, 99-110 (1999; Zbl 0944.65070)]. We further show that every local minimizer of the MPEC which satisfies the linear independence, upper level strict complementarity, and a second order optimality condition can be embedded into a locally unique piecewise smooth curve of local minimizers of the parametric NLP.


90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
90C31 Sensitivity, stability, parametric optimization
90C30 Nonlinear programming


Zbl 0944.65070
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