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DOI: 10.23952/cot.2024.2
Received December 3, 2022; Accepted May 4, 2023; Published October 2, 2023
Abstract. In this paper the generalized Minkowski sets are defined and characterized. On the other hand, the Motzkin decomposable sets, along with their epigraphic versions are considered and characterized in new ways. Among them, the closed convex sets with one single minimal face, i.e. translated closed convex cones, along with their epigraphic counterparts are particularly studied. Finally, the generalized Minkowski sets along with the class of closed convex sets with full Pareto like relative boundary are considered and studied. The latter ones are called Pareto bordered sets and their epigraphic counterparts are also considered and studied. It turns out that the Pareto bordered sets are generalized Minkowski.
How to Cite this Article:
J.E. Martínez-Legaz, C. Pintea, Closed convex sets of Motzkin, generalized Minkowski, and Pareto bordered types, Commun. Optim. Theory 2024 (2024) 2.