约束多项式Zonotopes
Constrained Polynomial Zonotopes
AI总结：
本文提出约束多项式Zonotopes这一非凸集表示法，证明其在多种集合运算下封闭且计算复杂度至多为多项式级别，并指出其推广了多种现有集表示法。
摘要：
我们引入了约束多项式Zonotopes，这是一种新颖的非凸集表示法，它在线性映射、Minkowski和、笛卡尔积、凸包、交集、并集以及二次和高阶映射下是封闭的。我们证明了约束多项式Zonotopes的上述集合运算的计算复杂度在表示大小上至多为多项式级别。约束多项式Zonotopes是Zonotopes、多胞体、多项式Zonotopes、Taylor模型和椭球体的推广，这一事实进一步证实了这种新集合表示法的相关性。从其他集合表示法转换为约束多项式Zonotopes在维度上至多为多项式级别。
英文摘要：
We introduce constrained polynomial zonotopes, a novel non-convex set representation that is closed under linear map, Minkowski sum, Cartesian product, convex hull, intersection, union, and quadratic as well as higher-order maps. We show that the computational complexity of the above-mentioned set operations for constrained polynomial zonotopes is at most polynomial in the representation size. The fact that constrained polynomial zonotopes are generalizations of zonotopes, polytopes, polynomial zonotopes, Taylor models, and ellipsoids, further substantiates the relevance of this new set representation. The conversion from other set representations to constrained polynomial zonotopes is at most polynomial with respect to the dimension.
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