Original title:
Hybrid Methods for Nonlinear Least Squares Problems
Authors:
Lukšan, Ladislav ; Matonoha, Ctirad ; Vlček, Jan Document type: Research reports
Year:
2019
Language:
eng Series:
Technical Report, volume: V-1246 Abstract:
This contribution contains a description and analysis of effective methods for minimization of the nonlinear least squares function F(x) = (1=2)fT (x)f(x), where x ∈ Rn and f ∈ Rm, 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:
hybrid methods; nonlinear least squares; numerical experiments; numerical optimization; partially separable problems; sparse problems; trust region methods
Rights: This work is protected under the Copyright Act No. 121/2000 Coll.