广义黏性逼近方法及其应用

doi:10.15960/j.cnki.issn.1007-6093.2020.03.010

运筹学学报 ›› 2020, Vol. 24 ›› Issue (3): 127-140.doi: 10.15960/j.cnki.issn.1007-6093.2020.03.010

广义黏性逼近方法及其应用

郭科^*, 王涛, 张有才

西华师范大学数学与信息学院, 四川南充 637009

收稿日期:2018-05-18 发布日期:2020-09-05
通讯作者: 郭科 E-mail:keguo2014@126.com
基金资助:
国家自然科学基金（Nos.11801455，11971238），中国博士后科学基金面上项目（Nos.2019M663459，2020T130081），四川省科技厅应用基础研究项目（No.2020YJ0111），西华师范大学国家一般培育项目（No.18B031）

Generalized viscosity approximation method and its application

GUO Ke^*, WANG Tao, Zhang Youcai

School of Mathematic and Information, China West Normal University, Nanchong 637009, Sichuan, China

Received:2018-05-18 Published:2020-09-05

摘要/Abstract

摘要： 黏性逼近方法在非扩张映射不动点问题的研究中扮演着重要的角色。提出了一类广义黏性逼近方法，在一定条件下，证明了该算法的收敛性.作为应用，将所得的收敛性结果应用于求解约束凸优化问题与双层优化问题。

关键词: 广义粘性逼近方法, 非扩张映射, 均值映射, 约束凸优化, 双层优化

Abstract: The viscosity approximation method plays an important role in the study of the fixed point problem of nonexpansive mappings. In this paper, we proposed a kind of generalized viscosity approximation method. Under certain conditions, we proved the convergence of the algorithm. As applications, we applied the obtained convergence results to solve the constrained convex optimization problems and the bilevel optimization problems.

Key words: generalized viscosity approximation method, nonexpansive mapping, averaged mapping, constrained convex optimization, bilevel optimization

中图分类号:

O221.2
O224

郭科, 王涛, 张有才. 广义黏性逼近方法及其应用[J]. 运筹学学报, 2020, 24(3): 127-140.

GUO Ke, WANG Tao, Zhang Youcai. Generalized viscosity approximation method and its application[J]. Operations Research Transactions, 2020, 24(3): 127-140.

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广义黏性逼近方法及其应用

Generalized viscosity approximation method and its application

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