- Hybrid methods for nonlinear least squares problems Ladislav Luksan(luksancs.cas.cz) Ctirad Matonoha(matonohacs.cas.cz) Jan Vlcek(vlcekcs.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: 05/17/2019Entry Accepted: 05/17/2019Entry Last Modified: 05/17/2019Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.