Accelerated Proximal Point Method for Maximally Monotone Operators

Abstract

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.

References in corpus (9)

• A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights
• An inertial forward-backward algorithm for monotone inclusions
• Optimized first-order methods for smooth convex minimization
• Exact Worst-case Performance of First-order Methods for Composite Convex Optimization
• Understanding the Acceleration Phenomenon via High-Resolution Differential Equations
• Another look at the fast iterative shrinkage/thresholding algorithm (FISTA)
• Generalizing the optimized gradient method for smooth convex minimization
• Optimal Nonergodic Sublinear Convergence Rate of Proximal Point Algorithm for Maximal Monotone Inclusion Problems
• On the Optimal Ergodic Sublinear Convergence Rate of the Relaxed Proximal Point Algorithm for Variational Inequalities

Cited by in corpus (6)

• Potential Function-based Framework for Making the Gradients Small in Convex and Min-Max Optimization
• Optimal Nonergodic Sublinear Convergence Rate of Proximal Point Algorithm for Maximal Monotone Inclusion Problems
• Bregman Augmented Lagrangian and Its Acceleration
• On the Optimal Ergodic Sublinear Convergence Rate of the Relaxed Proximal Point Algorithm for Variational Inequalities
• Halpern Iteration for Near-Optimal and Parameter-Free Monotone Inclusion and Strong Solutions to Variational Inequalities
• Fast convergence of generalized forward-backward algorithms for structured monotone inclusions