Tikhonov regularization of a second order dynamical system with Hessian driven damping

• 成果类型: Article
• 署名作者: Bot, Radu Ioan; Csetnek, Ernoe Robert; Laszlo, Szilard Csaba
• 署名单位: University of Vienna; Technical University of Cluj Napoca
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-020-01528-8
• 发表日期: 2021
• 页码: 151-186
• 关键词: evolution-equations; convex-optimization; monotone inclusions; inertial dynamics; CONVERGENCE

摘要

We investigate the asymptotic properties of the trajectories generated by a second-order dynamical system with Hessian driven damping and a Tikhonov regularization term in connection with the minimization of a smooth convex function in Hilbert spaces. We obtain fast convergence results for the function values along the trajectories. The Tikhonov regularization term enables the derivation of strong convergence results of the trajectory to the minimizer of the objective function of minimum norm.