A new one-step smoothing Newton method for nonlinear complementarity problem with \(P_{0}\)-function

DOI10.1016/j.amc.2010.02.001zbMath1239.65034OpenAlexW2021787570MaRDI QIDQ972151

Liang Fang

Publication date: 25 May 2010

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

Full work available at URL: https://doi.org/10.1016/j.amc.2010.02.001

zbMATH Keywords

algorithmglobal convergencenumerical experimentscoercivenesssmoothing Newton methodArmijo-type line searchnonlinear complementarity\(P_{0}\)-function

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33)

Related Items (14)

Nonmonotone smoothing inexact Newton method for the nonlinear complementarity problem ⋮ A smoothing Newton method for nonlinear complementarity problems ⋮ A smoothing Newton method for the second-order cone complementarity problem. ⋮ A generalized smoothing Newton method for the symmetric cone complementarity problem ⋮ Finite termination of a Newton-type algorithm for a class of affine variational inequality problems ⋮ A new interior-point algorithm for \(P_{\ast}(k)\)-NCP based on a class of parametric kernel functions ⋮ A new class of smoothing functions and a smoothing Newton method for complementarity problems ⋮ A family of new smoothing functions and~a~nonmonotone smoothing Newton method for the nonlinear complementarity problems ⋮ A smoothing inexact Newton method for nonlinear complementarity problems ⋮ A smoothing Newton method for ncps with the \(P_{0}\)-property ⋮ A smoothing Newton algorithm for solving the monotone second-order cone complementarity problems ⋮ A one-parametric class of smoothing functions and an improved regularization Newton method for the NCP ⋮ A regularization Newton method based on the generalized Fischer-Burmeister smoothing function for the NCP ⋮ A new class of neural networks for NCPs using smooth perturbations of the natural residual function

Cites Work

• Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications
• A regularization smoothing Newton method for solving nonlinear complementarity problem
• The convergence of a smoothing damped Gauss-Newton method for nonlinear complementarity problem
• Predictor-corrector smoothing Newton method, based on a new smoothing function, for solving the nonlinear complementarity problem with a \(P_0\) function
• A new look at smoothing Newton methods for nonlinear complementarity problems and box constrained variational inequalities
• A nonsmooth version of Newton's method
• The quadratic convergence of a smoothing Levenberg-Marquardt method for nonlinear complementarity problem
• A globally and superlinearly convergent smoothing Broyden-like method for solving nonlinear complementarity problem
• The convergence of a one-step smoothing Newton method for \(P_0\)-NCP based on a new smoothing NCP-function
• On P- and S-functions and related classes of \(n\)-dimensional nonlinear mappings
• Superlinear/quadratic one-step smoothing Newton method for \(P_0\)-NCP
• Semismooth and Semiconvex Functions in Constrained Optimization
• Smooth Approximations to Nonlinear Complementarity Problems
• Engineering and Economic Applications of Complementarity Problems
• Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations
• Improving the convergence of non-interior point algorithms for nonlinear complementarity problems
• A Global Linear and Local Quadratic Noninterior Continuation Method for Nonlinear Complementarity Problems Based on Chen--Mangasarian Smoothing Functions
• A Global and Local Superlinear Continuation-Smoothing Method forP₀andR₀NCP or Monotone NCP
• Finite-Dimensional Variational Inequalities and Complementarity Problems
• A new smoothing quasi-Newton method for nonlinear complementarity problems

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