Abstract
You are swimming close to an iceberg in the ocean. You calculate at what slope you have to swim down so that, whatever the direction in which you swim, you can be sure that you will not collide with the iceberg. We shall see that, provided that the lower surface of the iceberg is convex, this limiting slope is intimately related to the existence of subtangents to the iceberg that satisfy varions conditions. These considerations lead to generalizations of Rockafellar’s Maximal Monotonicity Theorem, and also of recent results on the existence of subtangents separating the epigraphs of proper convex lower semicontinuous functions from nonempty bounded closed convex sets.
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© 1995 Springer-Verlag Berlin Heidelberg
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Simons, S. (1995). Swimming below Icebergs. In: Maruyama, T., Takahashi, W. (eds) Nonlinear and Convex Analysis in Economic Theory. Lecture Notes in Economics and Mathematical Systems, vol 419. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-48719-4_20
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DOI: https://doi.org/10.1007/978-3-642-48719-4_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-58767-5
Online ISBN: 978-3-642-48719-4
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