Approximate Newton methods for nonsmooth equations

DOI10.1023/A:1022606224224zbMath0899.90150OpenAlexW1594115255MaRDI QIDQ1379958

J. Ning

Publication date: 5 March 1998

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1022606224224

zbMATH Keywords

superlinear convergencesemismooth equationsapproximate Newton methodsconsistently approximated JacobianLipschitz continuous equations

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Nonlinear programming (90C30) Nonsmooth analysis (49J52) Numerical computation of solutions to systems of equations (65H10)

Related Items

A two-step SOR-Newton method for nonsmooth equations, A generalized Jacobian based Newton method for semismooth block-triangular system of equations, Constructing a sequence of discrete Hessian matrices of an \(SC^{1}\) function uniformly convergent to the generalized Hessian matrix, A numerical method for interface reconstruction of triple points within a volume tracking algorithm, A system of nonsmooth equations solver based upon subgradient method, Some quadrature-based versions of the generalized Newton method for solving nonsmooth equations, A Newton collocation method for solving dynamic bargaining games, Solving variational inequality problems via smoothing-nonsmooth reformulations, Adaptive smoothing method, deterministically computable generalized Jacobians, and the Newton method, An approximate Newton method for non-smooth equations with finite max functions, On the convergence of modified Newton methods for solving equations containing a non-differentiable term, On a new class parametrized Newton-like method for semismooth equations, Point-Based Set-Valued Approximations, C -Differential Operators and Applications, Convergence analysis of nonsmooth equations for the general nonlinear complementarity problem, Computation of nonautonomous invariant and inertial manifolds, An approximate Newton method for solving non-smooth equations with infinite max functions, On the computation of an element of Clarke generalized Jacobian for a vector-valued max function, Convergence of the modified SOR–Newton method for non-smooth equations

Cites Work

• Unnamed Item
• An interior point algorithm of O\((\sqrt m| \ln\varepsilon |)\) iterations for \(C^ 1\)-convex programming
• A B-differentiable equation-based, globally and locally quadratically convergent algorithm for nonlinear programs, complementarity and variational inequality problems
• Nondifferential optimization via adaptive smoothing
• Local convergence of quasi-Newton methods for B-differentiable equations
• A parameterized Newton method and a quasi-Newton method for nonsmooth equations
• Superlinearly convergent approximate Newton methods for LC\(^ 1\) optimization problems
• A nonsmooth Newton method for variational inequalities. I: Theory
• A nonsmooth Newton method for variational inequalities. II: Numerical results
• Inexact Newton methods for solving nonsmooth equations
• Newton's method for the nonlinear complementarity problem: a B- differentiable equation approach
• A nonsmooth version of Newton's method
• Nonsmooth Equations: Motivation and Algorithms
• Newton's Method for B-Differentiable Equations
• Optimization and nonsmooth analysis
• EXTENSION OF NEWTON AND QUASI-NEWTON METHODS TO SYSTEMS OF PC^1 EQUATIONS
• Local structure of feasible sets in nonlinear programming, Part III: Stability and sensitivity
• Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations