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

Authors:
YU. Nesterov
Affiliations:
Center for Operations Research and Econometrics (CORE), Catholic University of Louvain (UCL), Louvain-la-Neuve, Belgium
Venue:
Optimization Methods & Software
Year:
2007

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Abstract

In this paper, we suggest a new version of the Gauss-Newton method for solving a system of non-linear equations which combines the idea of sharp merit function with the idea of quadratic regularization. For this scheme, we prove general convergence results and, under a natural non-degeneracy assumption, local quadratic convergence. We analyze the behavior of this scheme on a 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 standard convex optimization technique.