Affine scaling inexact generalized Newton algorithm with interior backtracking technique for solving bound-constrained semismooth equations

Authors:
Detong Zhu
Affiliations:
Department of Mathematics, Shanghai Normal University, Shanghai, P.R. China
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

Citing 10
Cited 0

A nonmonotone line search technique for Newton's method

SIAM Journal on Numerical Analysis
On concepts of directional differentiability

Journal of Optimization Theory and Applications
A nonsmooth version of Newton's method

Mathematical Programming: Series A and B
Convergence analysis of some algorithms for solving nonsmooth equations

Mathematics of Operations Research
Nonmonotonic trust region algorithm

Journal of Optimization Theory and Applications
On NCP-Functions

Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part II
Nonmonotone Trust-Region Methods for Bound-Constrained Semismooth Equations with Applications to Nonlinear Mixed Complementarity Problems

SIAM Journal on Optimization
An affine scaling trust-region approach to bound-constrained nonlinear systems

Applied Numerical Mathematics
An Interior Trust Region Approach for Nonlinear Minimization Subject to Bounds

An Interior Trust Region Approach for Nonlinear Minimization Subject to Bounds
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)

Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)

Quantified Score

Hi-index	7.29

Visualization

Abstract

We develop and analyze an affine scaling inexact generalized Newton algorithm in association with nonmonotone interior backtracking line technique for solving systems of semismooth equations subject to bounds on variables. By combining inexact affine scaling generalized Newton with interior backtracking line search technique, each iterate switches to inexact generalized Newton backtracking step to strict interior point feasibility. The global convergence results are developed in a very general setting of computing trial steps by the affine scaling generalized Newton-like method that is augmented by an interior backtracking line search technique projection onto the feasible set. Under some reasonable conditions we establish that close to a regular solution the inexact generalized Newton method is shown to converge locally p-order q-superlinearly, We characterize the order of local convergence based on convergence behavior of the quality of the approximate subdifferentials and indicate how to choose an inexact forcing sequence which preserves the rapid convergence of the proposed algorithm. A nonmonotonic criterion should bring about speeding up the convergence progress in some ill-conditioned cases.