A monotone semismooth Newton type method for a class of complementarity problems

DOI10.1016/j.cam.2010.08.012zbMath1204.65070OpenAlexW2128404944MaRDI QIDQ609212

Zhe Sun, Jin-ping Zeng

Publication date: 30 November 2010

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2010.08.012

zbMATH Keywords

numerical resultsnonsmooth equationsmonotone convergencecomplementarity problemsemismooth Newton method

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Methods of quasi-Newton type (90C53) Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33)

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Cites Work

• Unnamed Item
• Unnamed Item
• Free boundary problems with nonlinear source terms
• Free boundary problems in the theory of fluid flow through porous media: A numerical approach
• Iterative solution of large sparse systems of equations. Transl. from the German
• A semismooth equation approach to the solution of nonlinear complementarity problems
• A nonsmooth version of Newton's method
• A New Nonsmooth Equations Approach to Nonlinear Complementarity Problems
• Nonsmooth Equations: Motivation and Algorithms
• Newton's Method for B-Differentiable Equations
• The Primal-Dual Active Set Strategy as a Semismooth Newton Method
• Smoothing Methods and Semismooth Methods for Nondifferentiable Operator Equations
• Inexact semismooth Newton methods for large-scale complementarity problems
• Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations
• Parallel solutions of variational inequality problems with nonlinear source terms