论文标题
交替的线性最小化：重新审视冯·诺伊曼的交替预测
Alternating Linear Minimization: Revisiting von Neumann's alternating projections
论文作者
论文摘要
1933年，冯·诺伊曼（von Neumann）证明了一个美丽的结果，即通过交替的预测，即连续投影在一组上，然后是另一组。该算法假定一个集合可以访问投影操作员。在本说明中，我们考虑了较弱的设置，其中我们只能在凸组集合上访问线性最小化的orac，并提出算法以在两个凸集集的相交中找到一个点。
In 1933 von Neumann proved a beautiful result that one can approximate a point in the intersection of two convex sets by alternating projections, i.e., successively projecting on one set and then the other. This algorithm assumes that one has access to projection operators for both sets. In this note, we consider the much weaker setup where we have only access to linear minimization oracles over the convex sets and present an algorithm to find a point in the intersection of two convex sets.
