Linear separation theorems, besides being important results in Convex Ananysis, play a central role in the proofs of several central theorems in other fields. Morover, several results as such can be proven to be equivalent in themselves to a suitable separation theorem. In this paper we start analysing such a phenomenon, showing that the "Dual Cone" theorem between dual pairs of linear spaces implies several separation results, and that it can be exploited for several purposes, such as chatacterising both maxima of convex sets and aolutions of convex optimisation problems.

Dual Pairs and maximality

CASTAGNOLI, ERIO;FAVERO, GINO
2009

Abstract

Linear separation theorems, besides being important results in Convex Ananysis, play a central role in the proofs of several central theorems in other fields. Morover, several results as such can be proven to be equivalent in themselves to a suitable separation theorem. In this paper we start analysing such a phenomenon, showing that the "Dual Cone" theorem between dual pairs of linear spaces implies several separation results, and that it can be exploited for several purposes, such as chatacterising both maxima of convex sets and aolutions of convex optimisation problems.
2009
Dual Pairs and maximality
Castagnoli, Erio; Favero, Gino
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11565/3715414
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