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
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part II
An affine scaling trust-region approach to bound-constrained nonlinear systems
Applied Numerical Mathematics
Convergence of an inexact generalized Newton method with a scaled residual control
Computers & Mathematics with Applications
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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.