论文标题
均质锥：极性锥和投影
The Homogenization Cone: Polar Cone and Projection
论文作者
论文摘要
令$ c $是包含原始的真实希尔伯特空间的封闭凸子集，并假设$ k $是$ c $的均化锥，即，最小的封闭凸锥包含$ c \ times \ times \ {1 \} $。同质化锥在优化中起重要作用，因为它们包括二阶/洛伦兹/“冰淇淋”锥。 在本说明中，我们讨论了$ k $的极性锥体以及针对$ k $的投影的算法，前提是可以投影到$ c $。各种例子说明了我们的结果。
Let $C$ be a closed convex subset of a real Hilbert space containing the origin, and assume that $K$ is the homogenization cone of $C$, i.e., the smallest closed convex cone containing $C \times \{1\}$. Homogenization cones play an important role in optimization as they include, for instance, the second-order/Lorentz/"ice cream" cone. In this note, we discuss the polar cone of $K$ as well as an algorithm for finding the projection onto $K$ provided that the projection onto $C$ is available. Various examples illustrate our results.
