A robust semi-local convergence analysis of Newton's method for cone\n inclusion problems in Banach spaces under affine invariant majorant condition

2014/03/10 by O. P. Ferreira, Ferreira, Orizon P
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Mathematical and Theoretical Analysis #Numerical Analysis (math.NA) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1403.2462

openalex publication_date 2014/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A semi-local analysis of Newton's method for solving nonlinear inclusion\nproblems in Banach space is presented in this paper. Under a affine majorant\ncondition on the nonlinear function which is associated to the inclusion\nproblem, the robust convergence of the method and results on the convergence\nrate are established. Using this result we show that the robust analysis of the\nNewton's method for solving nonlinear inclusion problems under affine\nLipschitz-like and affine Smale's conditions can be obtained as a special case\nof the general theory. Besides for the degenerate cone, which the nonlinear\ninclusion becomes a nonlinear equation, ours analysis retrieve the classical\nresults on local analysis of Newton's method.\n

Citations

• Extension of Newton's method to nonlinear functions with values in a cone

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