1. Accelerated differential inclusion for convex optimization
- Author
-
Hao Luo
- Subjects
Lyapunov function ,Work (thermodynamics) ,Control and Optimization ,37M15, 34E10, 90C25 ,Applied Mathematics ,Management Science and Operations Research ,symbols.namesake ,Differential inclusion ,Optimization and Control (math.OC) ,ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION ,Convergence (routing) ,Convex optimization ,FOS: Mathematics ,Trajectory ,symbols ,Applied mathematics ,Proximal Gradient Methods ,Exponential decay ,Mathematics - Optimization and Control ,Mathematics - Abstract
This work 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 differential inclusion, both an inexact accelerated proximal point algorithm and an inexact accelerated proximal gradient method are proposed, and some new convergence rates are established via a discrete Lyapunov function.
- Published
- 2021