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Hybrid methods for nonlinear least squares problems

Ladislav Luksan(luksan***at***cs.cas.cz)
Ctirad Matonoha(matonoha***at***cs.cas.cz)
Jan Vlcek(vlcek***at***cs.cas.cz)

Abstract: This contribution contains a description and analysis of effective methods for minimization of the nonlinear least squares function $F(x) = (1/2) f^T(x) f(x)$, where $x \in R^n$ and $f \in R^m$, together with extensive computational tests and comparisons of the introduced methods. All hybrid methods are described in detail and their global convergence is proved in a unified way. Some proofs concerning trust region methods, which are difficult to find in the literature, are also added. In particular, the report contains an analysis of a new simple hybrid method with Jacobian corrections (Section~8) and an investigation of the simple hybrid method for sparse least squares problems proposed previously in [33] (Section~14).

Keywords: Numerical optimization, nonlinear least squares, trust region methods, hybrid methods, sparse problems, partially separable problems, numerical experiments

Category 1: Nonlinear Optimization (Nonlinear Systems and Least-Squares )

Category 2: Nonlinear Optimization (Unconstrained Optimization )

Citation: Technical Report V-1246, Institute of Computer Science AVCR, Prague, May 2019.

Download: [Postscript][Compressed Postscript][PDF]

Entry Submitted: 05/17/2019
Entry Accepted: 05/17/2019
Entry Last Modified: 05/17/2019

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