Optimality conditions for locally Lipschitz optimization with l(0)-regularization
Optimality conditions for locally Lipschitz optimization with l(0)-regularization
复制标题
使用 l(0)-正则化进行局部 Lipschitz 优化的最优条件
DOI：
10.1007/s11590-020-01579-y
复制
发表时间：
2021
影响因子：
1.6
通讯作者：
Xiu Naihua
中科院分区：
文献类型：
--
作者：
Zhang Hui;Pan Lili;Xiu Naihua
本文主要研究有限维空间中带正则化的局部Lipschitz优化问题（LLOP），该问题通常是NP难问题，但在统计、压缩感知和深度学习等领域具有很高的应用价值。首先，我们引入了两类稳定点：次微分稳定点和近似稳定点。其次，基于这两个概念，我们分析了正则化LLOP的一阶最优性充分必要条件。最后，我们给出了两个例子来说明所提出的最优性条件的有效性。
This paper mainly investigates thelocallyLipschitzoptimizationproblem (LLOP) with-regularization in a finite dimensional space, which is generally NP-hard but highly applicable in statistics, compressed sensing and deep learning. First, we introduce two classes of stationary points for this problem: subdifferential-stationary point and proximal-stationary point. Secondly, based on these two concepts, we analyze the first-order necessary/sufficient optimality conditions for the LLOP with-regularization. Finally, we present two examples to illustrate the validity of the proposed optimality conditions.