A primal-dual algorithm for minimizing a sum of Euclidean norms
Journal of Computational and Applied Mathematics
Quadratic one-step smoothing Newton method for P0-LCP without strict complementarity
Applied Mathematics and Computation
Applications of smoothing methods in numerical analysis and optimization
Focus on computational neurobiology
Smooth Convex Approximation to the Maximum Eigenvalue Function
Journal of Global Optimization
Smoothing-type algorithm for solving linear programs by using an augmented complementarity problem
Applied Mathematics and Computation
Computational Optimization and Applications
Journal of Computational and Applied Mathematics
A smoothing-type algorithm for solving system of inequalities
Journal of Computational and Applied Mathematics
A variant smoothing Newton method for P0-NCP based on a new smoothing function
Journal of Computational and Applied Mathematics
A smoothing conic trust region filter method for the nonlinear complementarity problem
Journal of Computational and Applied Mathematics
A nonmonotone smoothing Newton algorithm for solving nonlinear complementarity problems
Optimization Methods & Software
A regularized smoothing-type algorithm for solving a system of inequalities with a P0-function
Journal of Computational and Applied Mathematics
Smoothing algorithms for complementarity problems over symmetric cones
Computational Optimization and Applications
A new smoothing and regularization Newton method for P0-NCP
Journal of Global Optimization
Solvability of Newton equations in smoothing-type algorithms for the SOCCP
Journal of Computational and Applied Mathematics
A new hybrid method for nonlinear complementarity problems
Computational Optimization and Applications
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Based on Qi, Sun, and Zhou's smoothing Newton method, we propose a regularized smoothing Newton method for the box constrained variational inequality problem with P0-function (P0 BVI). The proposed algorithm generates an infinite sequence such that the value of the merit function converges to zero. If P0 BVI has a nonempty bounded solution set, the iteration sequence must be bounded. This result implies that there exists at least one accumulation point. Under CD-regularity, we prove that the proposed algorithm has a superlinear (quadratic) convergence rate without requiring strict complementarity conditions. The main feature of our global convergence results is that we do not assume a priori the existence of an accumulation point. This assumption is used widely in the literature due to the possible unboundedness of level sets of various adopted merit functions. Preliminary numerical results are also reported.