Lagrange Multipliers in Locally Convex Spaces

Mohammed Bachir () and Joël Blot ()
Additional contact information
Mohammed Bachir: Université Paris 1 Panthéon-Sorbonne
Joël Blot: Université Paris 1 Panthéon-Sorbonne

Journal of Optimization Theory and Applications, 2024, vol. 201, issue 3, No 12, 1275-1300

Abstract: Abstract We give a general Lagrange multiplier rule for mathematical programming problems in a Hausdorff locally convex space. We consider infinitely many inequality and equality constraints. Our results gives in particular a generalisation of the result of Jahn (Introduction to the theory of nonlinear optimization, Springer, Berlin, 2007), replacing Fréchet-differentiability assumptions on the functions by the Gateaux-differentiability. Moreover, the closed convex cone with a nonempty interior in the constraints is replaced by a strictly general class of closed subsets introduced in the paper and called “admissible sets”. Examples illustrating our results are given.

Keywords: Lagrange multipliers; Optimization problems; Admissible sets; Equi-Gateaux-differentiability; Primary 46N10; 49J50; Secondary 46G05 (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-024-02428-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:joptap:v:201:y:2024:i:3:d:10.1007_s10957-024-02428-z

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

DOI: 10.1007/s10957-024-02428-z

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 ().