AFSI: Adaptive Restart for Fast Semi-Iterative Schemes for Convex Optimisation

Abstract

Smooth optimisation problems arise in many fields including image processing, and having fast methods for solving them has clear benefits. Widely and successfully used strategies to solve them are accelerated gradient methods. They accelerate standard gradient-based schemes by means of extrapolation. Unfortunately, most acceleration strategies are generic, in the sense, that they ignore specific information about the objective function. In this paper, we implement an adaptive restarting into a recently proposed efficient acceleration strategy that was coined Fast Semi-Iterative (FSI) scheme. Our analysis shows clear advantages of the adaptive restarting in terms of a theoretical convergence rate guarantee and state-of-the-art performance on a challenging image processing task.