An Average Curvature Accelerated Composite Gradient Method for Nonconvex Smooth Composite Optimization Problems

DOI10.1137/19M1294277zbMath1458.90525arXiv1909.04248OpenAlexW3119028331MaRDI QIDQ5147027

Jiaming Liang, Renato D. C. Monteiro

Publication date: 2 February 2021

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

Full work available at URL: https://arxiv.org/abs/1909.04248

zbMATH Keywords

average curvaturefirst-order methodsiteration-complexityaccelerated composite gradient methodsline search free methodssmooth nonconvex composite programming

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Numerical mathematical programming methods (65K05) Nonconvex programming, global optimization (90C26) Nonlinear programming (90C30) Complexity and performance of numerical algorithms (65Y20)

Related Items

Average curvature FISTA for nonconvex smooth composite optimization problems, A FISTA-type accelerated gradient algorithm for solving smooth nonconvex composite optimization problems

Uses Software

• NC-OPT

Cites Work

• Smooth minimization of non-smooth functions
• A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
• Accelerated gradient methods for nonconvex nonlinear and stochastic programming
• Primal-dual first-order methods with \({\mathcal {O}(1/\varepsilon)}\) iteration-complexity for cone programming
• Introductory lectures on convex optimization. A basic course.
• Generalized uniformly optimal methods for nonlinear programming
• Efficiency of minimizing compositions of convex functions and smooth maps
• An Accelerated Hybrid Proximal Extragradient Method for Convex Optimization and Its Implications to Second-Order Methods
• Efficient Learning with a Family of Nonconvex Regularizers by Redistributing Nonconvexity
• Accelerated Methods for NonConvex Optimization
• Complexity of a Quadratic Penalty Accelerated Inexact Proximal Point Method for Solving Linearly Constrained Nonconvex Composite Programs
• Learning the parts of objects by non-negative matrix factorization
• Fast Gradient-Based Algorithms for Constrained Total Variation Image Denoising and Deblurring Problems
• Interior Gradient and Proximal Methods for Convex and Conic Optimization