Accelerated proximal point method for maximally monotone operators

This paper proposes an accelerated proximal point method for maximally monotone operators. The proof is computer-assisted via the performance estimation problem approach. The proximal point method includes various well-known convex optimization methods, such as the proximal method of multipliers and the alternating direction method of multipliers, and thus the proposed acceleration has wide applications. Numerical experiments are presented to demonstrate the accelerating behaviors.

Automated summary

This paper introduces an accelerated proximal point method for maximally monotone operators, with computer-assisted proof using the performance estimation problem approach. By incorporating various well-known convex optimization methods, such as the proximal method of multipliers and the alternating direction method of multipliers, the proposed acceleration technique has wide applications. Numerical experiments demonstrate the accelerating behavior of the method.