Unique solvability of weakly homogeneous generalized variational inequalities

Xueli Bai (), Mengmeng Zheng () and Zheng-Hai Huang ()
Additional contact information
Xueli Bai: South China Normal University
Mengmeng Zheng: Tianjin University
Zheng-Hai Huang: Tianjin University

Journal of Global Optimization, 2021, vol. 80, issue 4, No 8, 943 pages

Abstract: Abstract An interesting observation is that most pairs of weakly homogeneous mappings do not possess strongly monotonic property, which is one of the key conditions to ensure the unique solvability of the generalized variational inequality. This paper focuses on studying the uniqueness and solvability of the generalized variational inequality with a pair of weakly homogeneous mappings. By using a weaker condition than the strong monotonicity and some additional conditions, we achieve several results on the unique solvability to the underlying problem, which are exported by making use of the exceptional family of elements. As an adjunct, we also obtain the nonemptiness and compactness of the solution sets to the weakly homogeneous generalized variational inequality under some appropriate conditions. The conclusions presented in this paper are new or supplements to the existing ones even when the problem comes down to its important subclasses studied in recent years.

Keywords: Generalized variational inequality; Weakly homogeneous mapping; Exceptional family of elements; Degree theory; Strictly monotone mapping (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10898-021-01040-z 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:jglopt:v:80:y:2021:i:4:d:10.1007_s10898-021-01040-z

Ordering information: This journal article can be ordered from
http://www.springer. ... search/journal/10898

DOI: 10.1007/s10898-021-01040-z

Access Statistics for this article

Journal of Global Optimization is currently edited by Sergiy Butenko

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