A Perturbed Primal-Dual Dynamical System for Solving Convex-Concave Bilinear Saddle Point Problems
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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.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.
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图 1 不同的外源扰动函数ϵ选择下的收敛速率比较
注 为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.
Figure 1. Comparison of convergence rates with different exogenous disturbance functions ϵ
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