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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.

MSC:

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

Citations:

Zbl 0944.65070
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