论文标题
Heaviside设置受限优化：最佳和牛顿方法
Heaviside Set Constrained Optimization: Optimality and Newton Method
论文作者
论文摘要
现实世界中的数据经常涉及二进制状态：真相或虚假，积极性或负面，相似性或相似性，垃圾邮件或非垃圾邮件，并将其列举为回归，分类问题等。为了表征二进制状态，理想的功能之一是返回一个状态的重物步骤函数，另一种状态为零。因此，这是不连续性的。因此，处理二元状态的常规方法从其持续的替代物中受益匪浅。在本文中，我们直接针对Heaviside步骤功能，并研究Heaviside集的约束优化：计算可行集合的切线和正常锥体，建立了几种一阶足够和必要的最佳最佳条件，并开发了一种牛顿类型的方法，该方法可以在本地享受局部享受局部四边形的融合和出色的数字性能。
Data in the real world frequently involve binary status: truth or falsehood, positiveness or negativeness, similarity or dissimilarity, spam or non-spam, and to name a few, with applications into the regression, classification problems and so on. To characterize the binary status, one of the ideal functions is the Heaviside step function that returns one for one status and zero for the other. Hence, it is of dis-continuity. Because of this, the conventional approaches to deal with the binary status tremendously benefit from its continuous surrogates. In this paper, we target the Heaviside step function directly and study the Heaviside set constrained optimization: calculating the tangent and normal cones of the feasible set, establishing several first-order sufficient and necessary optimality conditions, as well as developing a Newton type method that enjoys locally quadratic convergence and excellent numerical performance.
