Hybrid Methods for Nonlinear Least Squares Problems

0504615 - ÚI 2020 CZ eng V - Výzkumná zpráva
Lukšan, Ladislav - Matonoha, Ctirad - Vlček, Jan
Hybrid Methods for Nonlinear Least Squares Problems.
Prague: ICS CAS, 2019. 50 s. Technical Report, V-1246.
Institucionální podpora: RVO:67985807
Klíčová slova: numerical optimization * nonlinear least squares * trust region methods * hybrid methods * sparse problems * partially separable problems * numerical experiments
Obor OECD: Applied mathematics

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).
Trvalý link: http://hdl.handle.net/11104/0296201