Modified Gauss-Newton scheme with worst-case guarantees for its global performance
(2007) Optimization Methods and Software — Vol. 22, n° 3, p. 469-483 (2007)
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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. (2007). Modified Gauss-Newton scheme with worst-case guarantees for its global performance. Optimization Methods and Software, 22(3), 469-483. https://doi.org/10.1080/08927020600643812 (Original work published 2007)