Weakly Convex Optimization over Stiefel Manifold Using Riemannian Subgradient-Type Methods
From MaRDI portal
Publication:5003207
DOI10.1137/20M1321000zbMath1505.65216arXiv1911.05047OpenAlexW3176493728WikidataQ115246903 ScholiaQ115246903MaRDI QIDQ5003207
Xiao Li, Zengde Deng, Qing Qu, Shixiang Chen, Zhihui Zhu, Anthony Man-Cho So
Publication date: 20 July 2021
Published in: SIAM Journal on Optimization (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1911.05047
nonconvex optimizationlinear convergenceiteration complexitydictionary learningorthogonality constraintmanifold optimizationrobust subspace recovery
Numerical mathematical programming methods (65K05) Large-scale problems in mathematical programming (90C06) Abstract computational complexity for mathematical programming problems (90C60) Nonconvex programming, global optimization (90C26)
Related Items
Tracking and Regret Bounds for Online Zeroth-Order Euclidean and Riemannian Optimization, Riemannian smoothing gradient type algorithms for nonsmooth optimization problem on compact Riemannian submanifold embedded in Euclidean space, Riemannian stochastic variance-reduced cubic regularized Newton method for submanifold optimization, A Dynamic Smoothing Technique for a Class of Nonsmooth Optimization Problems on Manifolds, A Riemannian Proximal Newton Method
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A feasible method for optimization with orthogonality constraints
- A new approach to the proximal point method: convergence on general Riemannian manifolds
- A splitting method for orthogonality constrained problems
- Subgradient algorithm on Riemannian manifolds
- Introductory lectures on convex optimization. A basic course.
- Subgradient methods for sharp weakly convex functions
- Riemannian proximal gradient methods
- A brief introduction to manifold optimization
- Nonconvex weak sharp minima on Riemannian manifolds
- A collection of nonsmooth Riemannian optimization problems
- Quadratic optimization with orthogonality constraint: explicit Łojasiewicz exponent and linear convergence of retraction-based line-search and stochastic variance-reduced gradient methods
- Efficiency of minimizing compositions of convex functions and smooth maps
- Robust computation of linear models by convex relaxation
- Generalized principal component analysis
- Iteration-complexity of gradient, subgradient and proximal point methods on Riemannian manifolds
- A generalized solution of the orthogonal Procrustes problem
- Non-existence of continuous convex functions on certain Riemannian manifolds
- Sparse Modeling for Image and Vision Processing
- A Vector-Contraction Inequality for Rademacher Complexities
- Generalized power method for sparse principal component analysis
- A Novel M-Estimator for Robust PCA
- A Riemannian Gradient Sampling Algorithm for Nonsmooth Optimization on Manifolds
- Finding a Sparse Vector in a Subspace: Linear Sparsity Using Alternating Directions
- Outlier-Robust PCA: The High-Dimensional Case
- Complete Dictionary Recovery Over the Sphere I: Overview and the Geometric Picture
- Complete Dictionary Recovery Over the Sphere II: Recovery by Riemannian Trust-Region Method
- Strong and Weak Convexity of Sets and Functions
- Weak Sharp Minima in Mathematical Programming
- Weak Sharp Minima on Riemannian Manifolds
- Robust Stochastic Approximation Approach to Stochastic Programming
- On convergence rates of subgradient optimization methods
- The Geometry of Algorithms with Orthogonality Constraints
- Variational Analysis
- Proximal Point Algorithm On Riemannian Manifolds
- Robust subspace recovery by Tyler's M-estimator
- Line Search Algorithms for Locally Lipschitz Functions on Riemannian Manifolds
- Stochastic Model-Based Minimization of Weakly Convex Functions
- Iteration-complexity of the subgradient method on Riemannian manifolds with lower bounded curvature
- A Well-Tempered Landscape for Non-convex Robust Subspace Recovery
- Global rates of convergence for nonconvex optimization on manifolds
- Exact and stable recovery of rotations for robust synchronization
- Proximal Gradient Method for Nonsmooth Optimization over the Stiefel Manifold
- Nonconvex Robust Low-Rank Matrix Recovery
- Fast, robust and non-convex subspace recovery
- A Robust Gradient Sampling Algorithm for Nonsmooth, Nonconvex Optimization
- Majorization for Changes in Angles Between Subspaces, Ritz Values, and Graph Laplacian Spectra
- Manifolds of Negative Curvature
