一个求解不可微凸优化问题的Perry-Shanno无记忆拟牛顿型方法  

A Perry-Shanno Memoryless Quasi-Newton-type Method for Nondifferentiable Convex Optimization

作　　者：李婉卿 欧宜贵[1] LI Wanqing;OU Yigui(School of Science,Hainan University,Haikou 570228,China)

机构地区：[1]海南大学理学院,海南海口570228

出　　处：《应用数学》2022年第4期880-891,共12页Mathematica Applicata

基　　金：Supported by NNSF(11961018);NSF of Hainan Province(120QN175)。

摘　　要：结合Perry-Shanno无记忆拟牛顿法、改进的线搜索方案和Moreau-Yosida正则化技术,本文提出一个可实施的求解不可微凸优化问题的Perry-Shanno无记忆拟牛顿型方法.在合理的假设下,我们建立了方法的整体收敛性.初步的数值实验结果表明了该方法的有效性.In this paper,an implementable Perry-Shanno memoryless quasi-Newton-type method for solving nondifferentiable convex optimization is proposed.It can be regarded as a combination of Moreau-Yosida regularization with a modified line search technique and the Perry-Shanno memoryless quasi-Newton method.Under some reasonable assumptions,the global convergence of the proposed method is established.Preliminary numerical results show that the proposed method is efficient in a sense.

关 键 词：非光滑优化 Moreau-Yosida正则化 Perry-Shanno无记忆拟牛顿法 全局收敛性 

分 类 号：O221.2[理学—运筹学与控制论]