A Globally Convergent LP-Newton Method

DOI10.1137/15M105241XzbMath1348.90583OpenAlexW2529842698MaRDI QIDQ2826818

Markus Herrich, Alexey F. Izmailov, Andreas Fischer, Mikhail V. Solodov

Publication date: 11 October 2016

Published in: SIAM Journal on Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/15m105241x

zbMATH Keywords

global convergencequadratic convergenceLP-Newton methodgeneralized Nash equilibrium problemsconstrained equations

Mathematics Subject Classification ID

Noncooperative games (91A10) Numerical methods based on necessary conditions (49M05) Newton-type methods (49M15) Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33)

Related Items

A decomposition method for a class of convex generalized Nash equilibrium problems ⋮ Semismooth Newton-type method for bilevel optimization: global convergence and extensive numerical experiments ⋮ A trust-region LP-Newton method for constrained nonsmooth equations under Hölder metric subregularity ⋮ Nonsingularity and stationarity results for quasi-variational inequalities ⋮ A modified inexact Levenberg-Marquardt method with the descent property for solving nonlinear equations ⋮ A special complementarity function revisited ⋮ On the local and superlinear convergence of a secant modified linear-programming-Newton method ⋮ A quasi-Newton modified LP-Newton method ⋮ Newton-type methods near critical solutions of piecewise smooth nonlinear equations ⋮ A family of inexact SQA methods for non-smooth convex minimization with provable convergence guarantees based on the Luo-Tseng error bound property ⋮ A globally convergent LP-Newton method for piecewise smooth constrained equations: escaping nonstationary accumulation points ⋮ Local convergence of the Levenberg-Marquardt method under Hölder metric subregularity ⋮ A Globally Convergent LP-Newton Method

Cites Work

• Unnamed Item
• An LP-Newton method: nonsmooth equations, KKT systems, and nonisolated solutions
• A new error bound result for generalized Nash equilibrium problems and its algorithmic application
• On error bounds and Newton-type methods for generalized Nash equilibrium problems
• Optimization reformulations of the generalized Nash equilibrium problem using Nikaido-Isoda-type functions
• Generalized Nash equilibrium problems and Newton methods
• Nonsmooth equations in optimization. Regularity, calculus, methods and applications
• Karush-Kuhn-Tucker systems: regularity conditions, error bounds and a class of Newton-type methods
• Stabilized sequential quadratic programming for optimization and a stabilized Newton-type method for variational problems
• A family of Newton methods for nonsmooth constrained systems with nonisolated solutions
• Improved error bound and a hybrid method for generalized Nash equilibrium problems
• A Globally Convergent LP-Newton Method
• On the solution of the KKT conditions of generalized Nash equilibrium problems
• Optimization and nonsmooth analysis
• Newton-Type Methods for Optimization Problems without Constraint Qualifications
• A Potential Reduction Newton Method for Constrained Equations
• Finite-Dimensional Variational Inequalities and Complementarity Problems
• Modified Wilson's Method for Nonlinear Programs with Nonunique Multipliers
• An Algorithm for Degenerate Nonlinear Programming with Rapid Local Convergence
• Newton-Type Methods for Optimization and Variational Problems
• Benchmarking optimization software with performance profiles.
• Convergence conditions for Newton-type methods applied to complementarity systems with nonisolated solutions