Mathematics of Operations Research
Some recent advances in projection-type methods for variational inequalities
Journal of Computational and Applied Mathematics - Proceedings of the international conference on recent advances in computational mathematics
Self-adaptive inexact proximal point methods
Computational Optimization and Applications
A non-interior-point smoothing method for variational inequality problem
Journal of Computational and Applied Mathematics
Smoothing Newton method for NCP with the identification of degenerate indices
Journal of Computational and Applied Mathematics
Optimizing revenue for bandwidth auctions over networks with time reservations
Computer Networks: The International Journal of Computer and Telecommunications Networking
A Derivative-Free Algorithm for Least-Squares Minimization
SIAM Journal on Optimization
A proximal point algorithm for the monotone second-order cone complementarity problem
Computational Optimization and Applications
On the local convergence of a derivative-free algorithm for least-squares minimization
Computational Optimization and Applications
On the convergence of an inexact Newton-type method
Operations Research Letters
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In this paper, we consider a proximal point algorithm (PPA) for solving monotone nonlinear complementarity problems (NCP). PPA generates a sequence by solving subproblems that are regularizations of the original problem. It is known that PPA has global and superlinear convergence properties under appropriate criteria for approximate solutions of subproblems. However, it is not always easy to solve subproblems or to check those criteria. In this paper, we adopt the generalized Newton method proposed by De Luca, Facchinei, and Kanzow to solve subproblems and adopt some NCP functions to check the criteria. Then we show that the PPA converges globally provided that the solution set of the problem is nonempty. Moreover, without assuming the local uniqueness of the solution, we show that the rate of convergence is superlinear in a genuine sense, provided that the limit point satisfies the strict complementarity condition.