Ekeland's principle and nuclear cones: a geometrical aspect

DOI10.1016/S0895-7177(97)00223-9zbMath1185.49018MaRDI QIDQ969761

B. E. Eshmatov

Publication date: 8 May 2010

Published in: Mathematical and Computer Modelling (Search for Journal in Brave)

Mathematics Subject Classification ID

Multi-objective and goal programming (90C29) Nonsmooth analysis (49J52) Applications of functional analysis in optimization, convex analysis, mathematical programming, economics (46N10) Applications of operator theory in optimization, convex analysis, mathematical programming, economics (47N10)

Related Items (17)

\(p\)-distances, \(q\)-distances and a generalized Ekeland's variational principle in uniform spaces ⋮ Ekeland's variational principle in locally convex spaces and the density of extremal points ⋮ Nuclear and full nuclear cones in product spaces: Pareto efficiency and an Ekeland type variational principle ⋮ Ekeland-Type Variational Principles and Equilibrium Problems ⋮ Nuclear cones in product spaces, pareto efficiency and Ekeland-type variational principles in locally convex spaces ⋮ The density of extremal points in Ekeland's variational principle ⋮ A general vectorial Ekeland's variational principle with a P-distance ⋮ Borwein-Preiss vector variational principle ⋮ A generalized vector-valued variational principle in Fréchet spaces ⋮ On semicomplete cones ⋮ Normality and nuclearity of convex cones ⋮ Pseudo-metric space and fixed point theorem ⋮ Local completeness and Pareto optimization ⋮ Full nuclear cones and a relation between strong optimization and Pareto efficiency ⋮ Local completeness, Pareto efficiency and Mackey Bishop-Phelps cones ⋮ A remark on Ekeland's principle in locally convex topological vector spaces. ⋮ Full nuclear cones associated to a normal cone. Application to Pareto efficiency.

Cites Work

• The strong Ekeland variational principle, the strong drop theorem and applications
• A characterization of proper minimal points as solutions of sublinear optimization problems
• Pareto optimization in infinite dimensional spaces: The importance of nuclear cones
• On the variational principle
• The variational principle and fixed point theorems in certain topological spaces
• The drop theorem, the petal theorem and Ekeland's variational principle
• Danes’ Drop Theorem in locally convex spaces
• Nonconvex minimization problems
• Equivalents of Ekeland's principle
• Stability Results for Ekeland's ε-Variational Principle and Cone Extremal Solutions
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