Tight Sublinear Convergence Rate of the Proximal Point Algorithm for Maximal Monotone Inclusion Problems

DOI10.1137/19M1299049zbMath1468.90083OpenAlexW3043533097MaRDI QIDQ3300773

Junfeng Yang, Guoyong Gu

Publication date: 30 July 2020

Published in: SIAM Journal on Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/19m1299049

zbMATH Keywords

semidefinite programmingproximal point algorithmmaximal monotone inclusionperformance estimation frameworktight sublinear convergence rate

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Semidefinite programming (90C22) Convex programming (90C25) Abstract computational complexity for mathematical programming problems (90C60) Numerical solution to inverse problems in abstract spaces (65J22)

Related Items (7)

Potential Function-Based Framework for Minimizing Gradients in Convex and Min-Max Optimization ⋮ Factor-\(\sqrt{2}\) acceleration of accelerated gradient methods ⋮ Fast Krasnosel’skiĭ–Mann Algorithm with a Convergence Rate of the Fixed Point Iteration of \(\boldsymbol{{ o} \left(\frac{1}{{ k}} \right)}\) ⋮ Branch-and-bound performance estimation programming: a unified methodology for constructing optimal optimization methods ⋮ Conic linear optimization for computer-assisted proofs. Abstracts from the workshop held April 10--16, 2022 ⋮ A unified and tight linear convergence analysis of the relaxed proximal point algorithm ⋮ Accelerated proximal point method for maximally monotone operators

Uses Software

• SeDuMi
• PESTO

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
• Optimized first-order methods for smooth convex minimization
• An optimal variant of Kelley's cutting-plane method
• Smooth strongly convex interpolation and exact worst-case performance of first-order methods
• On the convergence analysis of the optimized gradient method
• On the convergence rate of Douglas-Rachford operator splitting method
• Metric subregularity and the proximal point method
• Monotone (nonlinear) operators in Hilbert space
• On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators
• Produits infinis de resolvantes
• Exact worst-case convergence rates of the proximal gradient method for composite convex minimization
• On the worst-case complexity of the gradient method with exact line search for smooth strongly convex functions
• Performance of first-order methods for smooth convex minimization: a novel approach
• Multiplier and gradient methods
• On the Numerical Solution of Heat Conduction Problems in Two and Three Space Variables
• Splitting Algorithms for the Sum of Two Nonlinear Operators
• On the Convergence of the Proximal Point Algorithm for Convex Minimization
• New Proximal Point Algorithms for Convex Minimization
• Monotone Operators and the Proximal Point Algorithm
• Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming
• Using SeDuMi 1.02, A Matlab toolbox for optimization over symmetric cones
• Generalizing the Optimized Gradient Method for Smooth Convex Minimization
• Another Look at the Fast Iterative Shrinkage/Thresholding Algorithm (FISTA)
• Exact Worst-Case Performance of First-Order Methods for Composite Convex Optimization
• Convergence Rate Analysis of Several Splitting Schemes
• Faster Convergence Rates of Relaxed Peaceman-Rachford and ADMM Under Regularity Assumptions
• Proximité et dualité dans un espace hilbertien
• Convex Analysis
• Convex analysis and monotone operator theory in Hilbert spaces

This page was built for publication: Tight Sublinear Convergence Rate of the Proximal Point Algorithm for Maximal Monotone Inclusion Problems