Exact penalty functions in constrained optimization
SIAM Journal on Control and Optimization
A nonsmooth version of Newton's method
Mathematical Programming: Series A and B
Convergence analysis of some algorithms for solving nonsmooth equations
Mathematics of Operations Research
A Theoretical and Numerical Comparison of Some Semismooth Algorithms for Complementarity Problems
Computational Optimization and Applications
A New Merit Function For Nonlinear Complementarity Problems And A Related Algorithm
SIAM Journal on Optimization
Lagrangian Duality and Related Multiplier Methods for Variational Inequality Problems
SIAM Journal on Optimization
Dualization of Generalized Equations of Maximal Monotone Type
SIAM Journal on Optimization
Optimization Methods & Software
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In this paper, we present a new reformulation of the KKT system associated to a variational inequality as a semismooth equation. The reformulation is derived from the concept of differentiable exact penalties for nonlinear programming. The best theoretical results are presented for nonlinear complementarity problems, where simple, verifiable, conditions ensure that the penalty is exact. We close the paper with some preliminary computational tests on the use of a semismooth Newton method to solve the equation derived from the new reformulation. We also compare its performance with the Newton method applied to classical reformulations based on the Fischer-Burmeister function and on the minimum. The new reformulation combines the best features of the classical ones, being as easy to solve as the reformulation that uses the Fischer-Burmeister function while requiring as few Newton steps as the one that is based on the minimum.