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Modified Gauss-Newton scheme with worst case guarantees for global performance. (English) Zbl 1136.65051
A new modified version of the Gauss-Newton method for solving a system of nonlinear equations is presented. The proposed method is based on the combination of the idea of sharp merit function with the idea of quadratic regularization. The modified Gauss-Newton process is analyzed and general convergence results and, under a natural non-degeneracy assumption, local quadratic convergence, is proved.
The behaviour of the presented scheme is analyzed on a natural problem class for which global and local worst-case complexity bounds are taken. The implementation of each step of the scheme can be done by standard convex optimization technique. The results and the global efficiency of the method are compared with an existing technique.

MSC:
65H10 Numerical computation of solutions to systems of equations
65K05 Numerical mathematical programming methods
90C26 Nonconvex programming, global optimization
65Y20 Complexity and performance of numerical algorithms
90C51 Interior-point methods
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References:
[1] DOI: 10.1137/1.9780898719857 · Zbl 0958.65071
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