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A robust Kantorovich's theorem on inexact Newton method with relative residual error tolerance

O. P. Ferreira(orizon***at***mat.ufg.br)
B. F. Svaiter(benat***at***impa.br)

Abstract: We prove that under semi-local assumptions, the inexact Newton method with a fixed relative residual error tolerance converges Q-linearly to a zero of the non-linear operator under consideration. Using this result we show that Newton method for minimizing a self-concordant function or to find a zero of an analytic function can be implemented with a fixed relative residual error tolerance. In the absence of errors, our analysis retrieve the classical Kantorovich Theorem on Newton method.

Keywords: Kantorovich's theorem; Inexact Newton method; Banach space

Category 1: Nonlinear Optimization

Category 2: Infinite Dimensional Optimization


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Entry Submitted: 10/15/2011
Entry Accepted: 10/15/2011
Entry Last Modified: 10/15/2011

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