A Levenberg-Marquardt method with approximate projections

Research output: Contribution to journalResearch articleContributedpeer-review

Contributors

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

Original languageEnglish
Pages (from-to)5-26
Number of pages22
JournalComputational Optimization and Applications
Volume59
Issue number1-2
Publication statusPublished - 2014
Peer-reviewedYes

External IDs

Scopus 84906842248

Keywords

DFG Classification of Subject Areas according to Review Boards

Subject groups, research areas, subject areas according to Destatis

Keywords

  • Levenberg-Marquardt method, approximate projection, linear convergence

Library keywords