秩稀疏球的极值点不等式与几何
Extreme point inequalities and geometry of the rank sparsity ball
摘要：
我们研究了单位球的几何特征，单位球对应于矩阵的核范数与其元素的$l_1$范数之和-一种常见的罚函数，鼓励联合低秩和高稀疏性。作为这项工作的副产品，我们开发了一个微积分（或代数）的一般凸函数的面，产生一个简单而统一的方法来推导不等式平衡手头的最优化问题的各种功能，在解决方案集的极值点。
英文摘要：
We investigate geometric features of the unit ball corresponding to the sum of the nuclear norm of a matrix and the $l_1$ norm of its entries --- a common penalty function encouraging joint low rank and high sparsity. As a byproduct of this effort, we develop a calculus (or algebra) of faces for general convex functions, yielding a simple and unified approach for deriving inequalities balancing the various features of the optimization problem at hand, at the extreme points of the solution set.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
