Abstract
We introduce and study the class of weakly Motzkin predecomposable sets, which are those sets in ℝn that can be expressed as the Minkowski sum of a bounded convex set and a convex cone, none of them being necessarily closed. This class contains that of Motzkin predecomposable sets, for which the bounded components are compact, which in turn contains the class of Motzkin decomposable sets, for which the bounded components are compact and the conic components are closed.
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Acknowledgments
J. E. Martínez-Legaz was partially supported by the MINECO of Spain, Grant MTM2014-59179-C2-2-P, the Severo Ochoa Programme for Centres of Excellence in R&D [SEV-2015-0563], and under the Australian Research Council’s Discovery Projects funding scheme (project number DP140103213). He is affiliated with MOVE (Markets, Organizations and Votes in Economics). M. I. Todorov was partially supported by the MINECO of Spain and ERDF of EU, Grant MTM2014-59179-C2-1-P, and Sistema Nacional de Investigadores, Mexico.
We are grateful to the referees for helpful comments and pointing out some corrections. In particular, we are indebted to the referee who suggested us to consider the class of weakly Motzkin decomposable sets, a notion (s)he introduced in his/her report.
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Dedicated to Michel Théra on the occasion of his 70th birthday
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Martínez-Legaz, J.E., Todorov, M.I. Weakly Motzkin Predecomposable Sets. Set-Valued Var. Anal 25, 507–516 (2017). https://doi.org/10.1007/s11228-017-0420-0
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DOI: https://doi.org/10.1007/s11228-017-0420-0