Partial Smoothness and Constant Rank
Partial Smoothness and Constant Rank
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DOI：
10.1137/19m1237909
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发表时间：
2018-07
期刊：
影响因子：
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通讯作者：
A. Lewis;Jingwei Liang;Tonghua Tian
中科院分区：
文献类型：
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作者：
A. Lewis;Jingwei Liang;Tonghua Tian
优化中的部分光滑性思想融合了可行域和目标函数的某些光滑和非光滑性质。因此，标准的一阶条件保证了不同的迭代算法(和最优后分析)识别有效的结构或约束。然而，通过直接关注一阶条件，部分光滑性的形式概念大大简化了：在基本的微分几何语言中，它只是一个常数阶条件。在这个观点中，部分光滑性扩展到更一般的映射，例如原始-对偶分裂算法背后的鞍点算子。
The idea of partial smoothness in optimization blends certain smooth and nonsmooth properties of feasible regions and objective functions. As a consequence, the standard first-order conditions guarantee that diverse iterative algorithms (and post-optimality analyses) identify active structure or constraints. However, by instead focusing directly on the first-order conditions, the formal concept of partial smoothness simplifies dramatically: in basic differential geometric language, it is just a constant-rank condition. In this view, partial smoothness extends to more general mappings, such as saddlepoint operators underlying primal-dual splitting algorithms.