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

Nesterov, Yurii
(2003)

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  • Nesterov, YuriiUCLouvain
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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.
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Nesterov, Y. (2003). Modified Gauss-Newton scheme with worst-case guarantees for its global performance (CORE Discussion Papers 2003/86). https://hdl.handle.net/2078.5/129063