The rate of convergence of optimization algorithms obtained via discretizations of heavy ball dynamical systems for convex optimization problems. (9th December 2022)

• Record Type: Journal Article
• Authors: Alecsa, Cristian Daniel
• Is Part Of: Optimization. Volume 71:Number 13(2022)
• Page Start: 3909
• Page End: 3939
• Publication Date: 2022-12-09
• Subjects: Unconstrained optimization problems -- Nesterov gradient method -- convex function -- Hessian-driven damping -- dynamical system; 47J25 -- 90C25 -- 90C30 -- 65K10; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1925896
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we propose new numerical algorithms in the setting of unconstrained optimization problems and we prove the discrete rate of convergence of order O 1 / n 2 in the iterates of the convex objective function. Our optimization algorithms are obtained via discretizations from dynamical systems with Hessian-driven damping. Finally, some numerical experiments are presented in order to validate the theoretical results.