论文标题
约束多项式分子
Constrained Polynomial Zonotopes
论文作者
论文摘要
我们介绍了约束多项式分子，这是一种新型的非凸场表示，在线性图，Minkowski和，笛卡尔产物，凸出船体，交叉点，联合和二次图以及高阶图下封闭。我们表明，在表示大小中，最多多项式的上述集合操作的计算复杂性最多是多项式。受限的多项式分子构成的事实是地位，多元型，多项式界定，泰勒模型和椭圆形的概括，进一步证实了这一新集合表示的相关性。相对于维度，从其他集合表示到受约束多项式分子的转换最多是多项式。
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.
