Hybrid methods for nonlinear least squares problems
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  (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.
Entry Submitted: 05/17/2019
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