An Augmented Lagrangian method for quasi-equilibrium problems

L. F. Bueno (), G. Haeser (), F. Lara () and F. N. Rojas ()
Additional contact information
L. F. Bueno: Federal University of São Paulo
G. Haeser: University of São Paulo
F. Lara: Universidad de Tarapacá
F. N. Rojas: University of São Paulo

Computational Optimization and Applications, 2020, vol. 76, issue 3, No 6, 737-766

Abstract: Abstract In this paper, we propose an Augmented Lagrangian algorithm for solving a general class of possible non-convex problems called quasi-equilibrium problems (QEPs). We define an Augmented Lagrangian bifunction associated with QEPs, introduce a secondary QEP as a measure of infeasibility and we discuss several special classes of QEPs within our theoretical framework. For obtaining global convergence under a new weak constraint qualification, we extend the notion of an Approximate Karush–Kuhn–Tucker (AKKT) point for QEPs (AKKT-QEP), showing that in general it is not necessarily satisfied at a solution, differently from its counterpart in optimization. We study some particular cases where AKKT-QEP does hold at a solution, while discussing the solvability of the subproblems of the algorithm. We also present illustrative numerical experiments.

Keywords: Augmented Lagrangian methods; Quasi-equilibrium problems; Equilibrium problems; Constraint qualifications; Approximate-KKT conditions (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://link.springer.com/10.1007/s10589-020-00180-4 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:76:y:2020:i:3:d:10.1007_s10589-020-00180-4

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

DOI: 10.1007/s10589-020-00180-4

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 ().