On the convergence analysis of the optimized gradient method

DOI10.1007/s10957-016-1018-7zbMath1360.90200DBLPjournals/jota/KimF17arXiv1510.08573OpenAlexW2953231121WikidataQ47864275 ScholiaQ47864275MaRDI QIDQ511969

Jeffrey A. Fessler, Donghwan Kim

Publication date: 23 February 2017

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.08573

zbMATH Keywords

worst-case performance analysisconvergence boundfirst-order algorithmssmooth convex minimizationoptimized gradient method

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Semidefinite programming (90C22) Convex programming (90C25) Abstract computational complexity for mathematical programming problems (90C60) Nonlinear programming (90C30) Discrete approximations in optimal control (49M25)

Related Items (13)

A frequency-domain analysis of inexact gradient methods ⋮ Generalizing the Optimized Gradient Method for Smooth Convex Minimization ⋮ Adaptive restart of the optimized gradient method for convex optimization ⋮ An optimal gradient method for smooth strongly convex minimization ⋮ Factor-\(\sqrt{2}\) acceleration of accelerated gradient methods ⋮ Another Look at the Fast Iterative Shrinkage/Thresholding Algorithm (FISTA) ⋮ Efficient first-order methods for convex minimization: a constructive approach ⋮ Operator Splitting Performance Estimation: Tight Contraction Factors and Optimal Parameter Selection ⋮ Tight Sublinear Convergence Rate of the Proximal Point Algorithm for Maximal Monotone Inclusion Problems ⋮ Smooth strongly convex interpolation and exact worst-case performance of first-order methods ⋮ Optimizing the efficiency of first-order methods for decreasing the gradient of smooth convex functions ⋮ A piecewise conservative method for unconstrained convex optimization ⋮ Bilevel Methods for Image Reconstruction

Uses Software

• PESTO

Cites Work

• Smooth minimization of non-smooth functions
• 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
• Gradient methods for minimizing composite functions
• Smooth strongly convex interpolation and exact worst-case performance of first-order methods
• The exact information-based complexity of smooth convex minimization
• Introductory lectures on convex optimization. A basic course.
• Performance of first-order methods for smooth convex minimization: a novel approach
• Analysis and Design of Optimization Algorithms via Integral Quadratic Constraints
• Exact Worst-Case Performance of First-Order Methods for Composite Convex Optimization
• Some methods of speeding up the convergence of iteration methods

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