Scholtes, Stefan Convergence properties of a regularization scheme for mathematical programs with complementarity constraints. (English) Zbl 1010.90086 SIAM J. Optim. 11, No. 4, 918-936 (2001). 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. Cited in 7 ReviewsCited in 145 Documents MSC: 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) 90C31 Sensitivity, stability, parametric optimization 90C30 Nonlinear programming Keywords:complementarity constraints; regularization; B-stationarity Citations:Zbl 0944.65070 PDFBibTeX XMLCite \textit{S. Scholtes}, SIAM J. Optim. 11, No. 4, 918--936 (2001; Zbl 1010.90086) Full Text: DOI