Further on Inner Regularizations in Bilevel Optimization

M. Beatrice Lignola () and Jacqueline Morgan
Additional contact information
M. Beatrice Lignola: University of Naples Federico II, Napoli

Journal of Optimization Theory and Applications, 2019, vol. 180, issue 3, No 21, 1087-1097

Abstract: Abstract A crucial difficulty in pessimistic bilevel optimization is the possible lack of existence of exact solutions since marginal functions of the sup type may fail to be lower semicontinuous. So, to overcome this drawback, we have introduced, in Lignola and Morgan (J Optim Theory Appl 173(1):183–202, 2017), suitable inner regularizations of the lower level optimization problem together with relative viscosity solutions for the pessimistic bilevel problem. Here, we continue this research by considering new inner regularizations of the lower level optimization problem, which not necessarily satisfy the constraints but that are close to them, and by deriving an existence result of related viscosity solutions to the pessimistic bilevel problem.

Keywords: Pessimistic bilevel problem; Inner regularization; Viscosity solution; 49J45; 49J53; 90C47 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-018-1438-7 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:joptap:v:180:y:2019:i:3:d:10.1007_s10957-018-1438-7

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-018-1438-7

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

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