求解凸凹双线性鞍点问题的扰动原始对偶动力系统

何亮; 郭晓乐; 孙祥凯

doi:10.21656/1000-0887.450318

求解凸凹双线性鞍点问题的扰动原始对偶动力系统

doi: 10.21656/1000-0887.450318

重庆工商大学数学与统计学院，重庆 400067

基金项目:

重庆市自然科学基金（CSTB2024NSCQMSX0651）；重庆市研究生导师团队项目(yds223010）

详细信息

作者简介:
何亮（1999—），男，硕士生(E-mail: liangheee@126.com)；郭晓乐（1981—），女，副教授，博士(E-mail: xlguocqu1@163.com)；孙祥凯（1984—），男，教授，博士(通讯作者. E-mail: sunxk@ctbu.edu.cn).

通讯作者:
孙祥凯（1984—），男，教授，博士(通讯作者. E-mail: sunxk@ctbu.edu.cn).

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出版历程
- 收稿日期: 2024-11-25
- 修回日期: 2024-12-16
- 网络出版日期: 2025-09-10

A Perturbed Primal-Dual Dynamical System for Solving Convex-Concave Bilinear Saddle Point Problems

School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, P.R.China

摘要

摘要: 该文旨在研究求解凸凹双线性鞍点问题的一类带有外源扰动的二阶惯性原始对偶动力系统.首先, 建立了该系统全局强解的存在性和唯一性定理; 随后, 当扰动参数满足一定的可积条件时, 证明了原始对偶间隙函数和速度向量范数沿动力系统所产生解轨道的快速收敛速率.数值实验结果表明在不同的扰动情况下, 该动力系统均保持较快的收敛速率.
- 双线性鞍点问题 /
- 原始对偶动力系统 /
- 快速收敛速率
Abstract: A 2nd-order inertial primal-dual dynamical system with external perturbations for solving convex-concave bilinear saddle point problems was investigated. Firstly, the existence and uniqueness of the global strong solution of the dynamical system was established. Then, with integrable assumption on perturbation parameters, the fast convergence rates of the primal-dual gap function and the norms of velocity vectors along the trajectories generated by the dynamical system were obtained. Numerical experiments show that, the dynamical system has fast convergence rates under different kinds of perturbations.
- bilinear saddle point problem /
- primal-dual dynamical system /
- fast convergence rate

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参考文献(17)

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求解凸凹双线性鞍点问题的扰动原始对偶动力系统

doi: 10.21656/1000-0887.450318

作者简介:
何亮（1999—），男，硕士生(E-mail: liangheee@126.com)；郭晓乐（1981—），女，副教授，博士(E-mail: xlguocqu1@163.com)；孙祥凯（1984—），男，教授，博士(通讯作者. E-mail: sunxk@ctbu.edu.cn).

通讯作者:
孙祥凯（1984—），男，教授，博士(通讯作者. E-mail: sunxk@ctbu.edu.cn).

计量

A Perturbed Primal-Dual Dynamical System for Solving Convex-Concave Bilinear Saddle Point Problems

计量

目录

留言板

求解凸凹双线性鞍点问题的扰动原始对偶动力系统

doi: 10.21656/1000-0887.450318

作者简介: 何亮（1999—），男，硕士生(E-mail: liangheee@126.com)；郭晓乐（1981—），女，副教授，博士(E-mail: xlguocqu1@163.com)；孙祥凯（1984—），男，教授，博士(通讯作者. E-mail: sunxk@ctbu.edu.cn).

通讯作者: 孙祥凯（1984—），男，教授，博士(通讯作者. E-mail: sunxk@ctbu.edu.cn).

计量

出版历程

A Perturbed Primal-Dual Dynamical System for Solving Convex-Concave Bilinear Saddle Point Problems

计量

出版历程

目录

作者简介:
何亮（1999—），男，硕士生(E-mail: liangheee@126.com)；郭晓乐（1981—），女，副教授，博士(E-mail: xlguocqu1@163.com)；孙祥凯（1984—），男，教授，博士(通讯作者. E-mail: sunxk@ctbu.edu.cn).

通讯作者:
孙祥凯（1984—），男，教授，博士(通讯作者. E-mail: sunxk@ctbu.edu.cn).