Smoothing Newton and Quasi-Newton Methods for Mixed Complementarity Problems
Computational Optimization and Applications
Value functions and error bounds of trust region methods
Journal of Applied Mathematics and Computing
Error bound results for generalized D-gap functions of nonsmooth variational inequality problems
Journal of Computational and Applied Mathematics
Gap functions and global error bounds for set-valued variational inequalities
Journal of Computational and Applied Mathematics
Regularized gap functions for variational problems
Operations Research Letters
Gap functions and error bounds for quasi variational inequalities
Journal of Global Optimization
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New merit functions for variational inequality problems are constructed through the Moreau--Yosida regularization of some gap functions. The proposed merit functions constitute unconstrained optimization problems equivalent to the original variational inequality problem under suitable assumptions. Conditions are studied for those merit functions to be differentiable and for any stationary point of those functions to be a solution of the original variational inequality problem. Moreover, those functions are shown to provide global error bounds for general variational inequality problems under the strong monotonicity assumption only.