Abstract
We introduce and study the family of sets in a finite dimensional Euclidean space which can be written as the Minkowski sum of a compact and convex set and a convex cone (not necessarily closed). We establish several properties of the class of such sets, called Motzkin predecomposable, some of which hold also for the class of Motzkin decomposable sets (i.e., those for which the convex cone in the decomposition is requested to be closed), while others are specific of the new family.
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The work of A. N. Iusem was partially supported by CNPq Grant No. 301280/86.
J. E. Martínez-Legaz has been supported by the MICINN of Spain, Grant MTM2011-29064-C03-01. He is affiliated to MOVE (Markets, Organizations and Votes in Economics).
M. I. Todorov is on leave from IMI-BAS, Sofia, Bulgaria.
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Iusem, A.N., Martínez-Legaz, J.E. & Todorov, M.I. Motzkin predecomposable sets. J Glob Optim 60, 635–647 (2014). https://doi.org/10.1007/s10898-013-0097-3
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DOI: https://doi.org/10.1007/s10898-013-0097-3