Convergence conditions for Newton-type methods applied to complementarity systems with nonisolated solutions

Andreas Fischer (), Markus Herrich (), Alexey Izmailov () and Mikhail Solodov ()

Computational Optimization and Applications, 2016, vol. 63, issue 2, 425-459

Abstract: We consider a class of Newton-type methods that are designed for the difficult case when solutions need not be isolated, and the equation mapping need not be differentiable at the solutions. We show that the only structural assumption needed for rapid local convergence of those algorithms applied to PC $$^1$$ 1 -equations is the piecewise error bound, i.e., a local error bound holding for the branches of the solution set resulting from partitions of the bi-active complementarity indices. The latter error bound is implied by various piecewise constraint qualifications, including relatively weak ones. We apply our results to KKT systems arising from optimization or variational problems, and from generalized Nash equilibrium problems. In the first case, we show convergence if the dual part of the solution is a noncritical Lagrange multiplier, and in the second case convergence follows under a relaxed constant rank condition. In both cases, previously available results are improved. Copyright Springer Science+Business Media New York 2016

Keywords: Complementarity condition; KKT system; Error bound; Generalized Nash equilibrium problem; LP-Newton method; Levenberg–Marquardt method (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (8)

Downloads: (external link)
http://hdl.handle.net/10.1007/s10589-015-9782-0 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:coopap:v:63:y:2016:i:2:p:425-459

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-015-9782-0

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

More articles in Computational Optimization and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().