Riemannian Preconditioning

DOI10.1137/140970860zbMath1382.65180arXiv1405.6055OpenAlexW3037096902WikidataQ115246982 ScholiaQ115246982MaRDI QIDQ2792408

Bamdev Mishra, Rodolphe J. Sepulchre

Publication date: 9 March 2016

Published in: SIAM Journal on Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1405.6055

zbMATH Keywords

Lyapunov equationsequential quadratic programminggeneralized eigenvalue problemRiemannian optimizationlow rankGrassmannquotient manifoldmetric tuning

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Semidefinite programming (90C22) Nonlinear programming (90C30) Methods of successive quadratic programming type (90C55) Real-valued functions on manifolds (58C05)

Related Items (13)

Constraint optimization and SU(N) quantum control landscapes ⋮ Cholesky QR-based retraction on the generalized Stiefel manifold ⋮ Operator-valued formulas for Riemannian gradient and Hessian and families of tractable metrics in Riemannian optimization ⋮ Solving trust region subproblems using Riemannian optimization ⋮ Learning with symmetric positive definite matrices via generalized Bures-Wasserstein geometry ⋮ A multi-parameter family of metrics on Stiefel manifolds and applications ⋮ Geometric Matrix Midranges ⋮ Preconditioned Low-rank Riemannian Optimization for Linear Systems with Tensor Product Structure ⋮ Guarantees of Riemannian Optimization for Low Rank Matrix Recovery ⋮ Riemannian Stochastic Variance Reduced Gradient Algorithm with Retraction and Vector Transport ⋮ Unnamed Item ⋮ New Riemannian Preconditioned Algorithms for Tensor Completion via Polyadic Decomposition ⋮ Riemannian optimization with a preconditioning scheme on the generalized Stiefel manifold

Uses Software

• SDPLR
• Manopt
• RTRMC

Cites Work

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• Means and Averaging in the Group of Rotations
• Matrix Completion From a Few Entries
• Optimization algorithms exploiting unitary constraints

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