Convergence Analysis of the Proximal Gradient Method in the Presence of the Kurdyka–Łojasiewicz Property Without Global Lipschitz Assumptions
From MaRDI portal
Publication:6071886
DOI10.1137/23m1548293arXiv2301.05002OpenAlexW4388534080MaRDI QIDQ6071886
Xiaoxi Jia, Christian Kanzow, Patrick Mehlitz
Publication date: 29 November 2023
Published in: SIAM Journal on Optimization (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2301.05002
nonsmooth optimizationproximal gradient methodcomposite optimizationrate-of-convergencedesingularization functionKurdyka--Łojasiewicz propertynon-Lipschitzian optimization
Nonlinear programming (90C30) Numerical optimization and variational techniques (65K10) Nonsmooth analysis (49J52)
Cites Work
- Unnamed Item
- Unnamed Item
- A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
- On local convergence of the method of alternating projections
- An inertial forward-backward algorithm for the minimization of the sum of two nonconvex functions
- An inertial Tseng's type proximal algorithm for nonsmooth and nonconvex optimization problems
- Proximal alternating linearized minimization for nonconvex and nonsmooth problems
- On the convergence of the proximal algorithm for nonsmooth functions involving analytic features
- On the weak convergence of an ergodic iteration for the solution of variational inequalities for monotone operators in Hilbert space
- Ergodic convergence to a zero of the sum of monotone operators in Hilbert space
- On gradients of functions definable in o-minimal structures
- Local convergence of the heavy-ball method and iPiano for non-convex optimization
- A fast dual proximal gradient algorithm for convex minimization and applications
- The value function approach to convergence analysis in composite optimization
- Accelerating the DC algorithm for smooth functions
- Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward-backward splitting, and regularized Gauss-Seidel methods
- Convergence properties of monotone and nonmonotone proximal gradient methods revisited
- A dynamic alternating direction of multipliers for nonconvex minimization with nonlinear functional equality constraints
- Proximal gradient algorithms under local Lipschitz gradient continuity. A convergence and robustness analysis of PANOC
- iPiano: Inertial Proximal Algorithm for Nonconvex Optimization
- A concave optimization-based approach for sparse portfolio selection
- An Augmented Lagrangian Method for Non-Lipschitz Nonconvex Programming
- Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Łojasiewicz Inequality
- Linearly Constrained Non-Lipschitz Optimization for Image Restoration
- Clarke Subgradients of Stratifiable Functions
- From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images
- A generalized proximal point algorithm for certain non-convex minimization problems
- Monotone Operators and the Proximal Point Algorithm
- Variational Analysis
- Sparse Reconstruction by Separable Approximation
- Variational Analysis and Applications
- On $l_q$ Optimization and Matrix Completion
- First Order Methods Beyond Convexity and Lipschitz Gradient Continuity with Applications to Quadratic Inverse Problems
- Joint Power and Admission Control: Non-Convex <formula formulatype="inline"><tex Notation="TeX">$L_{q}$</tex></formula> Approximation and An Effective Polynomial Time Deflation Approach
- First-Order Methods in Optimization
- A New Augmented Lagrangian Method for MPCCs—Theoretical and Numerical Comparison with Existing Augmented Lagrangian Methods
- The Łojasiewicz Inequality for Nonsmooth Subanalytic Functions with Applications to Subgradient Dynamical Systems
- Convergence of the Iterates of Descent Methods for Analytic Cost Functions
- Convex Analysis
- A Descent Lemma Beyond Lipschitz Gradient Continuity: First-Order Methods Revisited and Applications
- Convex analysis and monotone operator theory in Hilbert spaces
- An augmented Lagrangian method for optimization problems with structured geometric constraints
- Constrained composite optimization and augmented Lagrangian methods