Precompact convergence of the nonconvex Primal-Dual Hybrid Gradient algorithm
Precompact convergence of the nonconvex Primal-Dual Hybrid Gradient algorithm
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DOI：
10.1016/j.cam.2017.07.037
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发表时间：
2018-03
期刊：
影响因子：
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通讯作者：
Tao Sun;R. Barrio;Lizhi Cheng;Hao Jiang
中科院分区：
文献类型：
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作者：
Tao Sun;R. Barrio;Lizhi Cheng;Hao Jiang
原始-对偶混合梯度(PDHG)算法是近年来用于解决鞍点优化问题的一种强有力的算法。经典的应用考虑了凸函数，在文献中得到了很好的研究。本文在预紧的假设下，考虑了非凸情形下PDHG算法的另一种形式的收敛问题。证明的基础是Kurdyka-Łojasiewic函数，它涵盖了广泛的问题。通过一个简单的数值实验说明了算法的收敛性质。
The Primal–Dual Hybrid Gradient (PDHG) algorithm is a powerful algorithm used quite frequently in recent years for solving saddle-point optimization problems. The classical application considers convex functions, and it is well studied in literature. In this paper, we consider the convergence of an alternative formulation of the PDHG algorithm in the nonconvex case under the precompact assumption. The proofs are based on the Kurdyka–Ł ojasiewic functions, that cover a wide range of problems. A simple numerical experiment illustrates the convergence properties.