Abstract
Convex sets separation is very important in convex programming, a very powerful mathematical tool for operations research, management and economics, for example. The target of this work is to present Theorem 3.1 that gives sufficient conditions for the strict separation of convex sets.
Highlights
The convex sets separation is very important in convex programming, a very powerful mathematical tool for, see [], operations research, management and economics, namely.In the mathematical fundamentals of the minimax theorem it is necessary to consider the strict separation of convex sets, see [ ]
Every closed convex set in a Hilbert space has only one point with minimal norm
Theorem 3.2 Being H a finite dimension Hilbert space, if A and B are non-empty disjoint convex sets, they can always be separated. As it was established in Theorem 3.1, it is enough that two closed convex sets are at finite distance from each other so that they can be strictly separated in the terms of the Definition 3.2
Summary
The convex sets separation is very important in convex programming, a very powerful mathematical tool for, see [. ], operations research, management and economics, namely. In the mathematical fundamentals of the minimax theorem it is necessary to consider the strict separation of convex sets, see [ ]. The target of this work is to present the Theorem 3.1 that gives sufficient conditions for the strict separation of convex sets. The results important to establish Theorem 3.1 are outlined in 2 and in 3 that theorem is present. Follow some conclusions and a short list of references
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