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- W4205514090 abstract "M -addition, denoted by ⊕ M , is a way of combining sets in a vector space which generalizes Minkowski addition +. Under certain circumstances Minkowski addition satisfies ( K ∩ L ) + C = ( K + C ) ∩ ( L + C ) and ( K ∪ L ) + ( K ∩ L ) = K + L . We prove parallel properties for M -addition and classify all compact sets M for which ( K ∪ L ) ⊕ M ( K ∩ L ) = K ⊕ M L . Minkowski addition also fulfills conv ( ∑ j = 1 m A j ) = ∑ j = 1 m conv A j , and we classify all sets M for which conv ( ⊕ M ( A 1 , … , A m ) ) = ⊕ conv M ( conv A 1 , … , conv A m ) , the natural M -addition generalization. Corollaries drawn from this result include conditions for when ⊕ M maps convex polytopes to convex polytopes and an extension of the Shapley–Folkman lemma to M -addition." @default.
- W4205514090 created "2022-01-25" @default.
- W4205514090 creator A5049169876 @default.
- W4205514090 date "2016-11-01" @default.
- W4205514090 modified "2023-09-29" @default.
- W4205514090 title "M-addition" @default.
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- W4205514090 doi "https://doi.org/10.1016/j.jmaa.2016.05.011" @default.
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