Abstract
Following an idea suggested by Rockafellar in his classical book on Convex Analysis, the first author defined in his doctoral thesis the enlarged space, by adjoining to the ordinary n-dimensional space “improper points” defined by directions, and developed a theory of convexity in such a space. Later the second author introduced a new model for the enlarged space, suitable for applying tools from the theory of cones, and closely related to the model that Rockafellar & Wets called “ray model” of the “cosmic closure” of the Euclidean space in their recent book on Variational Analysis. In this paper we introduce that model and use it to get some new theorems and proofs.
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© 2001 Springer-Verlag Berlin Heidelberg
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Hansen, G.L., Dupin, JC. (2001). Generalized Convexity for Unbounded Sets: The Enlarged Space. In: Hadjisavvas, N., Martínez-Legaz, J.E., Penot, JP. (eds) Generalized Convexity and Generalized Monotonicity. Lecture Notes in Economics and Mathematical Systems, vol 502. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56645-5_16
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DOI: https://doi.org/10.1007/978-3-642-56645-5_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41806-1
Online ISBN: 978-3-642-56645-5
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