Robust Accelerated Gradient Methods for Smooth Strongly Convex Functions

DOI10.1137/19M1244925zbMath1461.62145arXiv1805.10579OpenAlexW3008463948MaRDI QIDQ5853717

Alireza Fallah, Necdet Serhat Aybat, Asuman Ozdaglar, Mert Gürbüzbalaban

Publication date: 11 March 2021

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

Full work available at URL: https://arxiv.org/abs/1805.10579

zbMATH Keywords

convex optimizationstochastic approximationmatrix inequalitiesNesterov's methodrobust control theoryaccelerated methods

Mathematics Subject Classification ID

Convex programming (90C25) Nonlinear programming (90C30) Stochastic programming (90C15) Nonlinear systems in control theory (93C10) Linear systems in control theory (93C05) Stochastic approximation (62L20)

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Uses Software

• CVX

Cites Work

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• First-order methods of smooth convex optimization with inexact oracle
• An optimal method for stochastic composite optimization
• Stochastic intermediate gradient method for convex problems with stochastic inexact oracle
• Parameter-dependent Lyapunov functions and the discrete-time Popov criterion for robust analysis
• Introductory lectures on convex optimization. A basic course.
• The risk-sensitive index and the \(H_ 2\) and \(H_ \infty\) norms for nonlinear systems
• Couplings and quantitative contraction rates for Langevin dynamics
• Adaptive restart for accelerated gradient schemes
• The robust H/sub 2/ control problem: a worst-case design
• Smooth Optimization with Approximate Gradient
• Analysis and Design of Optimization Algorithms via Integral Quadratic Constraints
• Acceleration of Stochastic Approximation by Averaging
• Analysis of Optimization Algorithms via Integral Quadratic Constraints: Nonstrongly Convex Problems
• Polynomial Roots from Companion Matrix Eigenvalues
• Optimal Stochastic Approximation Algorithms for Strongly Convex Stochastic Composite Optimization I: A Generic Algorithmic Framework
• Optimal Stochastic Approximation Algorithms for Strongly Convex Stochastic Composite Optimization, II: Shrinking Procedures and Optimal Algorithms
• A Stochastic Approximation Method