Accelerated differential inclusion for convex optimization

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.

Keywords:

• Convex optimization
• inexact proximal point algorithm
• differential inclusion
• existence
• Lyapunov function

Disclosure statement

No potential conflict of interest was reported by the author(s).