Exact penalization and stationarity conditions of mathematical programs with equilibrium constraints
Mathematical Programming: Series A and B
Necessary optimality conditions for optimization problems with variational inequality constraints
Mathematics of Operations Research
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
Optimality Conditions for a Class of Mathematical Programs with Equilibrium Constraints
Mathematics of Operations Research
Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity
Mathematics of Operations Research
A Generalized Mathematical Program with Equilibrium Constraints
SIAM Journal on Control and Optimization
Exact Penalization and Necessary Optimality Conditions for Generalized Bilevel Programming Problems
SIAM Journal on Optimization
Optimality Conditions for Optimization Problems with Complementarity Constraints
SIAM Journal on Optimization
First-Order and Second-Order Conditions for Error Bounds
SIAM Journal on Optimization
Calmness of constraint systems with applications
Mathematical Programming: Series A and B
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Mathematical programs with equilibrium (or complementarity) constraints form a difficult class of optimization problems. The standard KKT conditions are not always necessary optimality conditions due to the fact that suitable constraint qualifications (CQs) are often violated. Alternatively, one can therefore use the Fritz John approach to derive necessary optimality conditions. While the usual Fritz John conditions do not provide much information, we prove an enhanced version of the Fritz John conditions. This version motivates the introduction of some new CQs which can then be used in order to obtain, for the first time, a completely elementary proof of the fact that a local minimum is an M-stationary point under one of these CQs. We also show how these CQs can be used to obtain a suitable exact penalty result under weaker or different assumptions than those that can be found in the literature.