Finding stationary points on bounded-rank matrices: a geometric hurdle and a smooth remedy
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Publication:6038660
DOI10.1007/s10107-022-01851-2arXiv2107.03877OpenAlexW3181949156WikidataQ114228487 ScholiaQ114228487MaRDI QIDQ6038660
Joe Kileel, Eitan Levin, Nicolas Boumal
Publication date: 2 May 2023
Published in: Mathematical Programming. Series A. Series B (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2107.03877
stationarityvariational analysistangent conesRiemannian optimizationClarke regularitylow-rank matricessingular algebraic varietiesnonsmooth sets
Nonconvex programming, global optimization (90C26) Numerical optimization and variational techniques (65K10) Optimality conditions and duality in mathematical programming (90C46) Set-valued and variational analysis (49J53)
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Cites Work
- Unnamed Item
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- Tensor-Train Decomposition
- Complexity bounds for second-order optimality in unconstrained optimization
- Concise complexity analyses for trust region methods
- Adaptive regularization with cubics on manifolds
- Correction to: ``On the continuity of the tangent cone to the determinantal variety
- Fixed-rank matrix factorizations and Riemannian low-rank optimization
- Optimality conditions for rank-constrained matrix optimization
- Tangent and normal cones for low-rank matrices
- Trust-region methods on Riemannian manifolds
- Low-Rank Matrix Completion by Riemannian Optimization
- Introduction to Smooth Manifolds
- Convergence Results for Projected Line-Search Methods on Varieties of Low-Rank Matrices Via Łojasiewicz Inequality
- Tensor Spaces and Numerical Tensor Calculus
- Low-Rank Matrix Approximation with Weights or Missing Data Is NP-Hard
- A Multilinear Singular Value Decomposition
- Global Optimality in Low-Rank Matrix Optimization
- An Introduction to Optimization on Smooth Manifolds
- Beyond Procrustes: Balancing-Free Gradient Descent for Asymmetric Low-Rank Matrix Sensing
- Global rates of convergence for nonconvex optimization on manifolds
- An Equivalence between Critical Points for Rank Constraints Versus Low-Rank Factorizations
- Finding Low-Rank Solutions via Nonconvex Matrix Factorization, Efficiently and Provably
- Gradient descent with non-convex constraints: local concavity determines convergence
- A Gradient Sampling Method on Algebraic Varieties and Application to Nonsmooth Low-Rank Optimization
- Desingularization of Bounded-Rank Matrix Sets
- Nonconvex Notions of Regularity and Convergence of Fundamental Algorithms for Feasibility Problems
- On critical points of quadratic low-rank matrix optimization problems
- Convex analysis and monotone operator theory in Hilbert spaces
