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

HE Liang; GUO Xiaole; SUN Xiangkai

doi:10.21656/1000-0887.450318

Volume 46 Issue 8

Aug. 2025

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Article Navigation > Applied Mathematics and Mechanics > 2025 > 46(8): 1064-1072

HE Liang, GUO Xiaole, SUN Xiangkai. A Perturbed Primal-Dual Dynamical System for Solving Convex-Concave Bilinear Saddle Point Problems[J]. Applied Mathematics and Mechanics, 2025, 46(8): 1064-1072. doi: 10.21656/1000-0887.450318

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

doi: 10.21656/1000-0887.450318

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

Received Date: 2024-11-25
Rev Recd Date: 2024-12-16

Available Online: 2025-09-10

Abstract

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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References

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