A Levenberg-Marquardt method with approximate projections

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung

Beitragende

Abstract

The projected Levenberg-Marquardt method for the solution of a system of equations with convex constraints is known to converge locally quadratically to a possibly nonisolated solution if a certain error bound condition holds. This condition turns out to be quite strong since it implies that the solution sets of the constrained and of the unconstrained system are locally the same.

Under a pair of more reasonable error bound conditions this paper proves R-linear convergence of a Levenberg-Marquardt method with approximate projections. In this way, computationally expensive projections can be avoided. The new method is also applicable if there are nonsmooth constraints having subgradients. Moreover, the projected Levenberg-Marquardt method is a special case of the new method and shares its R-linear convergence.

Details

OriginalspracheEnglisch
Seiten (von - bis)5-26
Seitenumfang22
FachzeitschriftComputational Optimization and Applications
Jahrgang59
Ausgabenummer1-2
PublikationsstatusVeröffentlicht - 2014
Peer-Review-StatusJa

Externe IDs

Scopus 84906842248

Schlagworte

DFG-Fachsystematik nach Fachkollegium

Fächergruppen, Lehr- und Forschungsbereiche, Fachgebiete nach Destatis

Schlagwörter

  • Levenberg-Marquardt method, approximate projection, linear convergence

Bibliotheksschlagworte