A multidimensional filter algorithm for nonlinear equations and nonlinear least-squares

Nick Gould; Sven Leyffer; Philippe Toint

doi:10.1137/S1052623403422637

A multidimensional filter algorithm for nonlinear equations and nonlinear least-squares

Nick Gould, Sven Leyffer, Philippe Toint

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Abstract

We introduce a new algorithm for the solution of systems of nonlinear equations and nonlinear least-squares problems that attempts to combine the efficiency of filter techniques and the robustness of trust-region methods. The algorithm is shown, under reasonable assumptions, to globally converge to zeros of the system, or to first-order stationary points of the Euclidean norm of its residual. Preliminary numerical experience is presented that shows substantial gains in efficiency over the traditional monotone trust-region approach. © 2004 Society for Industrial and Applied Mathematics.

Original language	English
Pages (from-to)	17-38
Number of pages	22
Journal	SIAM Journal on Optimization
Volume	15
Issue number	1
DOIs	https://doi.org/10.1137/S1052623403422637
Publication status	Published - 1 Jan 2005

Keywords

least-squares methods
filter methods
nonlinear equations
Nonlinear optimization
convergence theory

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.1137/S1052623403422637

45187Accepted author manuscript, 312 KB

Cite this

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A multidimensional filter algorithm for nonlinear equations and nonlinear least-squares

Abstract

Keywords

UN SDGs

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ADALGOPT: ADALGOPT - Advanced algorithms in nonlinear optimization

Filter methods for nonlinear problems

Cite this

A multidimensional filter algorithm for nonlinear equations and nonlinear least-squares

Abstract

Keywords

UN SDGs

Access to Document

Other files and links

Fingerprint

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ADALGOPT: ADALGOPT - Advanced algorithms in nonlinear optimization

Filter methods for nonlinear problems

Cite this