A generalized second-order derivative in nonsmooth optimization
SIAM Journal on Control and Optimization
An exact penalization viewpoint of constrained optimization
SIAM Journal on Control and Optimization
Growth behavior of a class of merit functions for the nonlinear complementarity problem
Journal of Optimization Theory and Applications
Exact penalization and stationarity conditions of mathematical programs with equilibrium constraints
Mathematical Programming: Series A and B
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
On the Calmness of a Class of Multifunctions
SIAM Journal on Optimization
Error Bounds for Lower Semicontinuous Functions in Normed Spaces
SIAM Journal on Optimization
A Unified Augmented Lagrangian Approach to Duality and Exact Penalization
Mathematics of Operations Research
Calmness and Error Bounds for Convex Constraint Systems
SIAM Journal on Optimization
Lagrange Multipliers and Calmness Conditions of Order p
Mathematics of Operations Research
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In this paper, we study KKT optimality conditions for constrained nonlinear programming problems and strong and Mordukhovich stationarities for mathematical programs with complementarity constraints using $l_p$ penalty functions, with $0\leq p\leq1$. We introduce some optimality indication sets by using contingent derivatives of penalty function terms. Some characterizations of optimality indication sets are obtained by virtue of the original problem data. We show that the KKT optimality condition holds at a feasible point if this point is a local minimizer of some $l_p$ penalty function with $p$ belonging to the optimality indication set. Our result on constrained nonlinear programming includes some existing results from the literature as special cases.