Extension of Quasi-Newton Methods to Mathematical Programs with Complementarity Constraints
Computational Optimization and Applications
A Trust-Region Method for Nonlinear Bilevel Programming: Algorithm and Computational Experience
Computational Optimization and Applications
Computational Optimization and Applications
A Robust SQP Method for Mathematical Programs with Linear Complementarity Constraints
Computational Optimization and Applications
Interior-Point Algorithms, Penalty Methods and Equilibrium Problems
Computational Optimization and Applications
Newton-Type method for a class of mathematical programs with complementarity constraints
Computers & Mathematics with Applications
Classification model selection via bilevel programming
Optimization Methods & Software - Mathematical programming in data mining and machine learning
Optimization and dynamical systems algorithms for finding equilibria of stochastic games
Optimization Methods & Software
A New Relaxation Scheme for Mathematical Programs with Equilibrium Constraints
SIAM Journal on Optimization
Combining the regularization strategy and the SQP to solve MPCC - A MATLAB implementation
Journal of Computational and Applied Mathematics
The C-Index: A New Stability Concept for Quadratic Programs with Complementarity Constraints
Mathematics of Operations Research
A smooth penalty approach and a nonlinear multigrid algorithm for elliptic MPECs
Computational Optimization and Applications
A Complementarity Framework for Forward Contracting Under Uncertainty
Operations Research
Mathematics of Operations Research
Computational Optimization and Applications
An $\ell_1$ Elastic Interior-Point Method for Mathematical Programs with Complementarity Constraints
SIAM Journal on Optimization
A smoothing-regularization approach to mathematical programs with vanishing constraints
Computational Optimization and Applications
A laminate parametrization technique for discrete ply-angle problems with manufacturing constraints
Structural and Multidisciplinary Optimization
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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 Fukushima and Pang [Convergence of a smoothing continuation method for mathematical programs with equilibrium constraints, in Ill-posed Variational Problems and Regularization Techniques, Springer-Verlag, New York, 1999]. 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.