论文标题
L0伪型的Capra-Convexity，凸出分解和变异配方
Capra-Convexity, Convex Factorization and Variational Formulations for the l0 Pseudonorm
论文作者
论文摘要
所谓的L0伪型或基数函数计算向量的非零组分的数量。在本文中，我们通过所谓的CAPRA（沿原始射线）共轭分析了L0伪型，为此，基本的源标准及其双重标准都是矫正单调的（我们正式引入了一个概念，并且涵盖了LP规范，但对于极端的概念）。 我们获得三个主要结果。首先，我们表明L0伪型等于其Capra-Biconjugate，即Capra-Convex函数。其次，我们推断出意外的后果，即我们称凸成分为：L0伪型在源规范的单位球体上重合，具有适当的凸较低的半连续函数。第三，我们通过通用的TOP-K双〜规范和k-Support dual〜规范（我们正式介绍）为L0伪型建立了一个变异公式。
The so-called l0 pseudonorm, or cardinality function, counts the number of nonzero components of a vector. In this paper, we analyze the l0 pseudonorm by means of so-called Capra (constant along primal rays) conjugacies, for which the underlying source norm and its dual norm are both orthant-strictly monotonic (a notion that we formally introduce and that encompasses the lp norms, but for the extreme ones). We obtain three main results. First, we show that the l0 pseudonorm is equal to its Capra-biconjugate, that is, is a Capra-convex function. Second, we deduce an unexpected consequence, that we call convex factorization: the l0 pseudonorm coincides, on the unit sphere of the source norm, with a proper convex lower semicontinuous function. Third, we establish a variational formulation for the l0 pseudonorm by means of generalized top-k dual~norms and k-support dual~norms (that we formally introduce).
