zbMATH — the first resource for mathematics

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.

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
Full Text: DOI
[1] DOI: 10.1137/1.9780898719857 · Zbl 0958.65071
[2] Dennis J. E., Numerical Methods for Unconstrained Optimization and Nonlinear Equations, 2. ed. (1996) · Zbl 0847.65038
[3] Ortega J. M., Iterative Solution of Nonlinear Equations in Several Variables (1970) · Zbl 0241.65046
[4] DOI: 10.1007/b98874 · Zbl 0930.65067
[5] DOI: 10.1007/s10107-006-0706-8 · Zbl 1142.90500
[6] Kantorovich L. V., Functional Analysis in Normed Spaces (1964) · Zbl 0127.06104
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.