In mathematical analysis, Ekeland's variational principle, discovered by Ivar Ekeland, is a theorem that asserts that there exist nearly optimal solutions to some optimization problems. Ekeland's principle can be used when the lower level set of a minimization problems is not compact, so that the … See more Ekeland was associated with the Paris Dauphine University when he proposed this theorem. See more • Caristi fixed-point theorem • Fenchel-Young inequality – the ("dual") lower-semicontinuous convex function resulting from the … See more Preliminary definitions A function $${\displaystyle f:X\to \mathbb {R} \cup \{-\infty ,+\infty \}}$$ valued in the extended real numbers See more • Ekeland, Ivar (1979). "Nonconvex minimization problems". Bulletin of the American Mathematical Society. New Series. 1 (3): 443–474. doi:10.1090/S0273-0979-1979-14595-6 See more WebEkeland Variational Principle (EkVP) [1] is one of the most important tools in nonlinear analysis that is used to minimize lower semicontinuous and bounded from below functions on a metric space ...
[PDF] The Ekeland variational principle for equilibrium problems ...
WebJun 22, 2024 · Download PDF Abstract: In this short communication, we present a generalization of the Ekeland variational principle. The main result is established through standard tools of functional analysis and calculus of variations. The novelty here is a result involving the second Gâteaux variation of the functional in question. WebJun 1, 2015 · This paper focuses on vector equilibrium problems whose final space is a real linear space not necessarily endowed with a topology, from which the Ekeland variational principles are derived by means of algebraic notions and a concept of approximate solution forvector equilibrium problems based on free-disposal sets. gold hinge bracelet
The Ekeland Variational Principle, the Bishop-Phelps …
WebEkeland's variational principle and the mountain pass lemma Shi Shuzhong 1 Acta Mathematica Sinica volume 1 , pages 348–355 ( 1985 ) Cite this article WebAbstract. For proper lower semicontinuous functionals bounded from below which do not increase upon polarization, an improved version of Ekeland’s variational principle can … WebSome versions of EkVP and Takahashi minimum principles in T1 quasi-metric spaces were proved in [10] and [2], respectively. In [10] the equivalence of the weak Ekeland variational principle to Caristi fixed point theorem was proved and the implications of the validity of Caristi fixed point theorem principle on the completeness of the underlying gold hinge boutique owner