On the convergence of the continuous gradient projection method

TL;DR

This paper proves convergence properties of the continuous gradient projection method and estimates its decay rate under certain conditions, advancing theoretical understanding of this optimization technique.

Contribution

It establishes weak and strong convergence of the method's trajectories and provides decay rate estimates when the objective function meets a Holderian error bound.

Findings

Proves weak and strong convergence of the method.

Provides decay rate estimates under Holderian error bounds.

Extends theoretical analysis of continuous gradient projection methods.

Abstract

We prove the weak and the strong convergence of the trajectories of the continuous gradient projection method under some mild assumptions on the objective function and the step size function. Moreover, we estimate the decay rate to equilibrium when the objective function satisfies a global Holderian error bound inequality.