The quadratic convergence of a smoothing Levenberg-Marquardt method for nonlinear complementarity problem

DOI10.1016/j.amc.2007.07.060zbMath1141.65044OpenAlexW2038859258MaRDI QIDQ2479227

Jia Tang, Chang-Feng Ma

Publication date: 26 March 2008

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

Full work available at URL: https://doi.org/10.1016/j.amc.2007.07.060

zbMATH Keywords

nonlinear complementarity problemLevenberg-Marquardt methodlocal quadratic convergencesmoothing functionleast \({l}_2\)-norm solution

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

Smoothing SQP algorithm for semismooth equations with box constraints, The Levenberg-Marquardt-type methods for a kind of vertical complementarity problem, Global complexity bound analysis of the Levenberg-Marquardt method for nonsmooth equations and its application to the nonlinear complementarity problem, A nonmonotone Levenberg-Marquardt method for nonlinear complementarity problems under local error bound, A new one-step smoothing Newton method for nonlinear complementarity problem with \(P_{0}\)-function, Convergence analysis of nonmonotone Levenberg-Marquardt algorithms for complementarity problem, A smoothing self-adaptive Levenberg-Marquardt algorithm for solving system of nonlinear inequalities, A note on the Levenberg-Marquardt parameter, The convergence of a smoothing damped Gauss-Newton method for nonlinear complementarity problem

Cites Work

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• Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications
• A globally convergent Levenberg-Marquardt method for solving nonlinear complementarity problem
• Convergence theory for the structured BFGS secant method with an application to nonlinear least squares
• Factorized quasi-Newton methods for nonlinear least squares problems
• Merit functions for semi-definite complementarity problems
• Solution of monotone complementarity problems with locally Lipschitzian functions
• Nonmonotone Levenberg-Marquardt algorithms and their convergence analysis
• Non-interior continuation methods for solving semidefinite complementarity problems
• Non-interior continuation method for solving the monotone semidefinite complementarity problem
• A class of smoothing functions for nonlinear and mixed complementarity problems
• A new look at smoothing Newton methods for nonlinear complementarity problems and box constrained variational inequalities
• The Global Linear Convergence of a Noninterior Path-Following Algorithm for Linear Complementarity Problems
• A Noninterior Continuation Method for Quadratic and Linear Programming
• On Homotopy-Smoothing Methods for Box-Constrained Variational Inequalities
• Global and superlinear convergence of the smoothing Newton method and its application to general box constrained variational inequalities
• A Family of Scaled Factorized Broyden-Like Methods for Nonlinear Least Squares Problems
• Some Noninterior Continuation Methods for Linear Complementarity Problems
• Solving variational inequality problems via smoothing-nonsmooth reformulations