Critical sets in parametric optimization
Mathematical Programming: Series A and B
Numerical continuation methods: an introduction
Numerical continuation methods: an introduction
Exact Penalization of Mathematical Programs with Equilibrium Constraints
SIAM Journal on Control and Optimization
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part II
Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity
Mathematics of Operations Research
Mathematics of Operations Research
SIAM Journal on Optimization
Extension of Quasi-Newton Methods to Mathematical Programs with Complementarity Constraints
Computational Optimization and Applications
BI-Level Strategies in Semi-Infinite Programming
BI-Level Strategies in Semi-Infinite Programming
An Interior Point Method for Mathematical Programs with Complementarity Constraints (MPCCs)
SIAM Journal on Optimization
A Robust SQP Method for Mathematical Programs with Linear Complementarity Constraints
Computational Optimization and Applications
Local Convergence of SQP Methods for Mathematical Programs with Equilibrium Constraints
SIAM Journal on Optimization
Interior-Point Algorithms, Penalty Methods and Equilibrium Problems
Computational Optimization and Applications
Nonlinear Optimization in Finite Dimensions - Morse Theory, Chebyshev Approximation, Transversality, Flows, Parametric Aspects (Nonconvex Optimization and its Applications Volume 47)
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B
SIAM Journal on Optimization
Lifting mathematical programs with complementarity constraints
Mathematical Programming: Series A and B
Characterization of strong stability for C-stationary points in MPCC
Mathematical Programming: Series A and B
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We introduce nondegeneracy and the C-index for C-stationary points of a QPCC, that is, for a mathematical program with a quadratic objective function and linear complementarity constraints. The C-index characterizes the qualitative local behavior of a QPCC around a nondegenerate C-stationary point. The article focuses on the structure of the C-stationary set of QPCCs depending on a real parameter. We show that, for generic QPCC data, the C-index changes exactly at turning points of the C-stationary set, and that it changes by exactly one. To illustrate this concept, we introduce and analyze two homotopy methods for finding C-stationary points. Numerical results illustrate that, for randomly generated test problems, the two homotopy methods very often identify B-stationary points.