eng
Lukšan, Ladislav
Matonoha, Ctirad
Vlček, Jan
Hybrid Methods for Nonlinear Least Squares Problems
numerical optimization
nonlinear least squares
trust region methods
hybrid methods
sparse problems
partially separable problems
numerical experiments
http://hdl.handle.net/11104/0296201
http://www.nusl.cz/ntk/nusl-395920
http://invenio.nusl.cz/record/395920/files/content.csg.pdf
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).
2019