An Invariant-Point Theorem in Banach Space with Applications to Nonconvex Optimization

Vo Si Trong Long ()
Additional contact information
Vo Si Trong Long: University of Science

Journal of Optimization Theory and Applications, 2022, vol. 194, issue 2, No 3, 440-464

Abstract: Abstract An invariant-point theorem and its equivalent formulation are established in which distance functions are replaced by minimal time functions. It is worth emphasizing here that the class of minimal time functions can be interpreted as a general type of directional distance functions recently used to develop new applications in optimization theory. The obtained results are applied in two directions. First, we derive sufficient conditions for the existence of solutions to optimization-related problems without convexity. As an easy corollary, we get a directional Ekeland variational principle. Second, we propose a new type of global error bounds for inequalities which allows us to simultaneously study nonconvex and convex functions. Several examples and comparison remarks are included as well to explain advantages of our results with existing ones in the literature.

Keywords: Minimal time functions; Invariant points; Existence of solutions; Generalized global error bounds; 49J53; 90C26; 49J27; 58E30 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-022-02033-y 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:194:y:2022:i:2:d:10.1007_s10957-022-02033-y

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

DOI: 10.1007/s10957-022-02033-y

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 ().