Tikhonov Regularization of Second-order plus First-order Primal-dual Dynamical Systems for Separable Convex Optimization

Xiangkai Sun (), Lijuan Zheng () and Kok Lay Teo ()
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Xiangkai Sun: Chongqing Key Laboratory of Statistical Intelligent Computing and Monitoring, College of Mathematics and Statistics, Chongqing Technology and Business University
Lijuan Zheng: Chongqing Key Laboratory of Statistical Intelligent Computing and Monitoring, College of Mathematics and Statistics, Chongqing Technology and Business University
Kok Lay Teo: School of Mathematical Sciences, Sunway University

Journal of Optimization Theory and Applications, 2025, vol. 207, issue 1, No 12, 36 pages

Abstract: Abstract This paper deals with a Tikhonov regularized second-order plus first-order primal-dual dynamical system with time scaling for separable convex optimization problems with linear equality constraints. This system consists of two second-order ordinary differential equations for the primal variables and one first-order ordinary differential equation for the dual variable. By utilizing the Lyapunov analysis approach, we obtain the convergence properties of the primal-dual gap, the objective function error, the feasibility measure and the gradient norm of the objective function along the trajectory. We also establish the strong convergence of the primal trajectory generated by the dynamical system towards the minimal norm solution of the separable convex optimization problem. Furthermore, we give numerical experiments to illustrate the theoretical results, showing that our dynamical system performs better than those in the literature in terms of convergence rates.

Keywords: Separable convex optimization; Tikhonov regularization; Convergence rate; Primal-dual dynamical system; 90C25; 37N40; 34D05 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02766-6

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