Accelerated differential inclusion for convex optimization. (4th May 2023)

• Record Type: Journal Article
• Authors: Luo, Hao
• Is Part Of: Optimization. Volume 72:Number 5(2023)
• Page Start: 1139
• Page End: 1170
• Publication Date: 2023-05-04
• Subjects: Convex optimization -- inexact proximal point algorithm -- differential inclusion -- existence -- Lyapunov function; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.2002327
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : This paper introduces a second-order differential inclusion for unconstrained convex optimization. In continuous level, solution existence in proper sense is obtained and exponential decay of a novel Lyapunov function along with the solution trajectory is derived as well. Then in discrete level, based on numerical discretizations of the continuous model, two inexact proximal point algorithms are proposed, and some new convergence rates are established via a discrete Lyapunov function.