Optimality conditions based on the Fréchet second-order subdifferential

D. T. V. An () and N. D. Yen ()
Additional contact information
D. T. V. An: Thai Nguyen University of Sciences
N. D. Yen: Vietnam Academy of Science and Technology

Journal of Global Optimization, 2021, vol. 81, issue 2, No 4, 365 pages

Abstract: Abstract This paper focuses on second-order necessary optimality conditions for constrained optimization problems on Banach spaces. For problems in the classical setting, where the objective function is $$C^2$$ C 2 -smooth, we show that strengthened second-order necessary optimality conditions are valid if the constraint set is generalized polyhedral convex. For problems in a new setting, where the objective function is just assumed to be $$C^1$$ C 1 -smooth and the constraint set is generalized polyhedral convex, we establish sharp second-order necessary optimality conditions based on the Fréchet second-order subdifferential of the objective function and the second-order tangent set to the constraint set. Three examples are given to show that the used hypotheses are essential for the new theorems. Our second-order necessary optimality conditions refine and extend several existing results.

Keywords: Constrained optimization problems on Banach spaces; Second-order necessary optimality conditions; Fréchet second-order subdifferential; Second-order tangent set; Generalized polyhedral convex set; 49K27; 49J53; 90C30; 90C46; 90C20 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10898-021-01011-4 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:jglopt:v:81:y:2021:i:2:d:10.1007_s10898-021-01011-4

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

DOI: 10.1007/s10898-021-01011-4

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 ().