An analogue of the Krein-Milman theorem for star-shaped sets.
Martini, Horst, Wenzel, Walter (2003)
Beiträge zur Algebra und Geometrie
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Martini, Horst, Wenzel, Walter (2003)
Beiträge zur Algebra und Geometrie
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Fedorchuk, V.V. (2009)
Sibirskij Matematicheskij Zhurnal
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Borwein, Jonathan, Lucet, Yves, Mordukhovich, Boris (2000)
Journal of Convex Analysis
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V. V. Fedorchuk (2009)
Matematički Vesnik
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Kharazishvili, A. (2003)
Georgian Mathematical Journal
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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.
Khusainov, A.A. (2001)
Sibirskij Matematicheskij Zhurnal
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Jan Ratajski (1993)
Colloquium Mathematicae
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Let X be the three-dimensional, complete, nonsingular, complex torus embedding corresponding to a fan 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.
Dalla, Leoni, Samiou, Evangelia (2007)
Beiträge zur Algebra und Geometrie
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Gubarev, V.Yu. (2009)
Sibirskij Matematicheskij Zhurnal
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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...
Martini, Horst, Wenzel, Walter (2004)
Beiträge zur Algebra und Geometrie
Similarity: