The effect of smooth parametrizations on nonconvex optimization landscapes
DOI10.1007/s10107-024-02058-3MaRDI QIDQ6665380
Eitan Levin, Nicolas Boumal, Joe Kileel
Publication date: 17 January 2025
Published in: Mathematical Programming. Series A. Series B (Search for Journal in Brave)
overparametrizationoptimization on manifoldsstrict saddlesbenign nonconvexityHadamard parametrization of simplexlow rank optimizationsymmetries in landscapes
Nonconvex programming, global optimization (90C26) Optimality conditions and duality in mathematical programming (90C46) Set-valued and variational analysis (49J53) Operations research, mathematical programming (90-XX) Applications of differential geometry to data and computer science (53Z50)
Cites Work
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- Tensor Decompositions and Applications
- A fresh variational-analysis look at the positive semidefinite matrices world
- The role of duality in optimization problems involving entropy functionals with applications to information theory
- A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization
- The cochlioid.
- Concise complexity analyses for trust region methods
- The Schur complement and its applications
- Second-order optimality and beyond: characterization and evaluation complexity in convexly constrained nonlinear optimization
- Topological properties of the set of functions generated by neural networks of fixed size
- Fixed-rank matrix factorizations and Riemannian low-rank optimization
- Tangent and normal cones for low-rank matrices
- First-order methods almost always avoid strict saddle points
- Local minima and convergence in low-rank semidefinite programming
- Convergence Results for Projected Line-Search Methods on Varieties of Low-Rank Matrices Via Łojasiewicz Inequality
- Low-Rank Optimization on the Cone of Positive Semidefinite Matrices
- The Geometry of Algorithms with Orthogonality Constraints
- An Introduction to Optimization on Smooth Manifolds
- Learning deep linear neural networks: Riemannian gradient flows and convergence to global minimizers
- Deterministic Guarantees for Burer‐Monteiro Factorizations of Smooth Semidefinite Programs
- An Equivalence between Critical Points for Rank Constraints Versus Low-Rank Factorizations
- Information Geometry
- Desingularization of Bounded-Rank Matrix Sets
- Finding stationary points on bounded-rank matrices: a geometric hurdle and a smooth remedy
- From the simplex to the sphere: faster constrained optimization using the Hadamard parametrization
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