Displaying similar documents to “Conjugacy for closed convex sets.”

Extensions of convex functionals on convex cones

E. Ignaczak, A. Paszkiewicz (1998)

Applicationes Mathematicae

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We prove that under some topological assumptions (e.g. if M has nonempty interior in X), a convex cone M in a linear topological space X is a linear subspace if and only if each convex functional on M has a convex extension on the whole space X.

On the Betti numbers of the real part of a three-dimensional torus embedding

Jan Ratajski (1993)

Colloquium Mathematicae

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Let X be the three-dimensional, complete, nonsingular, complex torus embedding corresponding to a fan S 3 and let V be the real part of X (for definitions see [1] or [3]). The aim of this note is to give a simple combinatorial formula for calculating the Betti numbers of V.

On localizing global Pareto solutions in a given convex set

Agnieszka Drwalewska, Lesław Gajek (1999)

Applicationes Mathematicae

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Sufficient conditions are given for the global Pareto solution of the multicriterial optimization problem to be in a given convex subset of the domain. In the case of maximizing real valued-functions, the conditions are sufficient and necessary without any convexity type assumptions imposed on the function. In the case of linearly scalarized vector-valued functions the conditions are sufficient and necessary provided that both the function is concave and the scalarization is increasing...