Modified Gauss-Newton scheme with worst-case guarantees for its global performance

Yu Nesterov

No 2003086, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: In this paper we suggest a new version of Gauss-Newton method for solving a system of nonlinear equations, which combines the idea of a sharp merit function with the idea of a quadratic regularization. For this scheme we prove general convergence results and, under a natural non-degeneracy assumption, a local quadratic convergence. We analyze the behavior of this scheme on some natural problem class, for which we get global and local worst-case complexity bounds. The implementation of each step of the scheme can be done by a standard convex optimization technique.

Keywords: systems of nonlinear equations; Gauss-Newton method; trust-region methods; complexity bounds; global rate of convergence (search for similar items in EconPapers)
Date: 2003-12
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