Proximal gradient algorithms under local Lipschitz gradient continuity. A convergence and robustness analysis of PANOC

DOI10.1007/s10957-022-02048-5zbMath1495.65078arXiv2112.13000OpenAlexW4286631413MaRDI QIDQ2159445

Alberto De Marchi, Andreas Themelis

Publication date: 1 August 2022

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

Full work available at URL: https://arxiv.org/abs/2112.13000

zbMATH Keywords

forward-backward splittingnonsmooth nonconvex optimizationlinesearch methodslocally Lipschitz gradient

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Nonlinear programming (90C30)

Related Items

Convergence Analysis of the Proximal Gradient Method in the Presence of the Kurdyka–Łojasiewicz Property Without Global Lipschitz Assumptions ⋮ Constrained composite optimization and augmented Lagrangian methods ⋮ A Regularized Newton Method for \({\boldsymbol{\ell}}_{q}\) -Norm Composite Optimization Problems

Uses Software

• ALGENCAN
• UNLocBoX
• GitHub
• Alpaqa
• ProximalAlgorithms.jl
• PANOC
• OpEn

Cites Work

• Unnamed Item
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• UNLocBoX
• PANOC
• Further properties of the forward-backward envelope with applications to difference-of-convex programming
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• Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming
• Variational Analysis
• First Order Methods Beyond Convexity and Lipschitz Gradient Continuity with Applications to Quadratic Inverse Problems
• Forward-Backward Envelope for the Sum of Two Nonconvex Functions: Further Properties and Nonmonotone Linesearch Algorithms
• Relatively Smooth Convex Optimization by First-Order Methods, and Applications
• Convergence of Inexact Forward--Backward Algorithms Using the Forward--Backward Envelope
• The Variable Metric Forward-Backward Splitting Algorithm Under Mild Differentiability Assumptions
• Practical Augmented Lagrangian Methods for Constrained Optimization
• A Bregman Forward-Backward Linesearch Algorithm for Nonconvex Composite Optimization: Superlinear Convergence to Nonisolated Local Minima
• OpEn