Analytical convergence regions of accelerated gradient descent in nonconvex optimization under regularity condition

DOI10.1016/j.automatica.2019.108715zbMath1440.93071arXiv1810.03229OpenAlexW2997973415WikidataQ126466333 ScholiaQ126466333MaRDI QIDQ2173914

Huaqing Xiong, Bin Hu, Wei Zhang, Yuejie Chi

Publication date: 17 April 2020

Published in: Automatica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.03229

zbMATH Keywords

robust controlnonconvex optimizationregularity conditionaccelerated gradient descent

Mathematics Subject Classification ID

Sensitivity (robustness) (93B35) Nonconvex programming, global optimization (90C26)

Related Items (3)

A frequency-domain analysis of inexact gradient methods ⋮ A zeroing neural dynamics based acceleration optimization approach for optimizers in deep neural networks ⋮ Convergence of gradient algorithms for nonconvex \(C^{1+ \alpha}\) cost functions

Uses Software

• Wirtinger Flow

Cites Work

• Unnamed Item
• On the Kalman-Yakubovich-Popov lemma
• Introductory lectures on convex optimization. A basic course.
• Analysis of biased stochastic gradient descent using sequential semidefinite programs
• Phase Retrieval via Wirtinger Flow: Theory and Algorithms
• Solving Random Quadratic Systems of Equations Is Nearly as Easy as Solving Linear Systems
• Analysis and Design of Optimization Algorithms via Integral Quadratic Constraints
• Solving Systems of Random Quadratic Equations via Truncated Amplitude Flow
• On Fienup Methods for Sparse Phase Retrieval
• The Role of Convexity in Saddle-Point Dynamics: Lyapunov Function and Robustness
• Analysis of Optimization Algorithms via Integral Quadratic Constraints: Nonstrongly Convex Problems
• Non-convex low-rank matrix recovery with arbitrary outliers via median-truncated gradient descent
• Continuous-Time Accelerated Methods via a Hybrid Control Lens
• The Proximal Augmented Lagrangian Method for Nonsmooth Composite Optimization
• Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overview
• Matrix Completion From a Few Entries
• Some methods of speeding up the convergence of iteration methods
• Robust Accelerated Gradient Methods for Smooth Strongly Convex Functions

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