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  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
Positivity – Springer Journals
Published: Apr 1, 2004
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