Inexact Newton's method to nonlinear functions with values in a cone

2015/10/07 by O. P. Ferreira, Ferreira, O. P., G. N. Silva +1
Mathematics · Computer Science · #Iterative Methods for Nonlinear Equations #Advanced Optimization Algorithms Research #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1510.01947

Abstract

The problem of finding a solution of nonlinear inclusion problems in Banach space is considered in this paper. Using convex optimization techniques introduced by Robinson (Numer. Math., Vol. 19, 1972, pp. 341-347), a robust convergence theorem for inexact Newton's method is proved. As an application, an affine invariant version of Kantorovich's theorem and Smale's α-theorem for inexact Newton's method is obtained.

Citations

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

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