Augmented Lagrangian and exact penalty methods for quasi-variational inequalities

Christian Kanzow () and Daniel Steck ()
Additional contact information
Christian Kanzow: University of Würzburg
Daniel Steck: University of Würzburg

Computational Optimization and Applications, 2018, vol. 69, issue 3, No 8, 824 pages

Abstract: Abstract A variant of the classical augmented Lagrangian method was recently proposed in Kanzow (Math Program 160(1–2, Ser. A):33–63, 2016), Pang and Fukushima (Comput Manag Sci 2(1):21–56, 2005) for the solution of quasi-variational inequalities (QVIs). In this paper, we describe an improved convergence analysis to the method. In particular, we introduce a secondary QVI as a new optimality concept for quasi-variational inequalities and use this tool to prove convergence theorems for certain popular classes of QVIs under very mild assumptions. Finally, we present a modification of the augmented Lagrangian method which turns out to be an exact penalty method, and also give detailed numerical results illustrating the performance of both methods.

Keywords: Quasi-variational inequality; Augmented Lagrangian method; Global convergence; Feasibility; Exact penalty (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://link.springer.com/10.1007/s10589-017-9963-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:69:y:2018:i:3:d:10.1007_s10589-017-9963-0

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

DOI: 10.1007/s10589-017-9963-0

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 ().