Equivalent formulations of Ekeland's variational principle

DOI10.1016/j.na.2003.07.009zbMath1029.49019OpenAlexW1999926010MaRDI QIDQ1412234

Z. L. Wu

Publication date: 10 November 2003

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2003.07.009

zbMATH Keywords

error boundsfixed point theoremEkeland's variational principleweak sharp minima\({\varepsilon}\)-condition of Hamel\({\varepsilon}\)-condition of Takahashi

Mathematics Subject Classification ID

Set-valued and variational analysis (49J53) Fixed-point and coincidence theorems (topological aspects) (54H25) Existence theories for problems in abstract spaces (49J27)

Related Items (13)

\(p\)-distances, \(q\)-distances and a generalized Ekeland's variational principle in uniform spaces ⋮ New vectorial versions of Takahashi's nonconvex minimization problem ⋮ Ekeland's variational principle in locally convex spaces and the density of extremal points ⋮ A generalized Ekeland vector variational principle and its applications in optimization ⋮ Some equivalent formulations of the generalized Ekeland's variational principle and their applications ⋮ A general vectorial Ekeland's variational principle with a P-distance ⋮ Vectorial form of Ekeland-type variational principle in locally convex spaces and its applications ⋮ On regularity concepts in variational analysis ⋮ A generalized vector-valued variational principle in Fréchet spaces ⋮ Equivalent extensions to Caristi-Kirk's fixed point theorem, Ekeland's variational principle, and Takahashi's minimization theorem ⋮ Maximality principle and general results of Ekeland and Caristi types without lower semicontinuity assumptions in cone uniform spaces with generalized pseudodistances ⋮ Error bounds and metric subregularity ⋮ Some Dual Conditions for Global Weak Sharp Minimality of Nonconvex Functions

Cites Work

• Unnamed Item
• On the variational principle
• Error Bounds for Lower Semicontinuous Functions in Normed Spaces
• The drop theorem, the petal theorem and Ekeland's variational principle
• Nonconvex minimization problems
• Fixed Points and Stationary Points of Dissipative Multivalued Maps
• Fixed Point Theorems for Mappings Satisfying Inwardness Conditions
• Remarks to an equivalent formulation of ekeland’s variational principle

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