Nuclear and Full Nuclear Cones in Product Spaces: Pareto Efficiency and an Ekeland Type Variational Principle

Nuclear and Full Nuclear Cones in Product Spaces: Pareto Efficiency and an Ekeland Type... Positivity (2005) 9:511–539 © Springer 2005 DOI 10.1007/s11117-004-2770-8 Nuclear and Full Nuclear Cones in Product Spaces: Pareto Efficiency and an Ekeland Type Variational Principle 1 2 G. ISAC and CHR. TAMMER Department of Mathematics, Royal Military College of Canada, PO Box 17000, STN; FORCES, Kingston, Ontario, Canada, K7K 7B4; Fachbereich Mathematik und Informatik, Institut Fur ¨ Optimierung und Stochastik, Martin-Luther-Universitat, ¨ Halle-Wittenberg, Theodor-Lieser Str. 5, D-06099 Halle, Germany 1. Introduction In this paper we will consider a relation between the nuclearity for cones, the Pareto efficiency and the Ekeland’s Variational Principle. The variational principle discovered by I. Ekeland in 1972 [16] is among the most important results obtained in Non-linear Analysis and it has sig- nificant applications in Optimization, Optimal Control Theory, Game The- ory, in the study of dynamical systems etc. [15–20, 25–29, 47, 48]. It is well known that this principle is equivalent to the Caristi–Kirk Fixed-Point Theorem, to the Drop Theorem and to the Petal Theorem [21, 22, 29, 39, 44]. Many authors have been considered Ekeland’s Principle from several points of view, on metric spaces [1, 8–10, 15–20, 22, 29, 44], in locally convex topological vector spaces [10, 35] and also in general topo- logical http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Nuclear and Full Nuclear Cones in Product Spaces: Pareto Efficiency and an Ekeland Type Variational Principle

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2005 by Springer
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-004-2770-8
Publisher site
See Article on Publisher Site

Abstract

Positivity (2005) 9:511–539 © Springer 2005 DOI 10.1007/s11117-004-2770-8 Nuclear and Full Nuclear Cones in Product Spaces: Pareto Efficiency and an Ekeland Type Variational Principle 1 2 G. ISAC and CHR. TAMMER Department of Mathematics, Royal Military College of Canada, PO Box 17000, STN; FORCES, Kingston, Ontario, Canada, K7K 7B4; Fachbereich Mathematik und Informatik, Institut Fur ¨ Optimierung und Stochastik, Martin-Luther-Universitat, ¨ Halle-Wittenberg, Theodor-Lieser Str. 5, D-06099 Halle, Germany 1. Introduction In this paper we will consider a relation between the nuclearity for cones, the Pareto efficiency and the Ekeland’s Variational Principle. The variational principle discovered by I. Ekeland in 1972 [16] is among the most important results obtained in Non-linear Analysis and it has sig- nificant applications in Optimization, Optimal Control Theory, Game The- ory, in the study of dynamical systems etc. [15–20, 25–29, 47, 48]. It is well known that this principle is equivalent to the Caristi–Kirk Fixed-Point Theorem, to the Drop Theorem and to the Petal Theorem [21, 22, 29, 39, 44]. Many authors have been considered Ekeland’s Principle from several points of view, on metric spaces [1, 8–10, 15–20, 22, 29, 44], in locally convex topological vector spaces [10, 35] and also in general topo- logical

Journal

PositivitySpringer Journals

Published: Apr 1, 2004

References

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