Continuation Methods for Riemannian Optimization

DOI10.1137/21M1428650WikidataQ115246855 ScholiaQ115246855MaRDI QIDQ5081103

Daniel Kressner, Axel Séguin

Publication date: 1 June 2022

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

Full work available at URL: https://arxiv.org/abs/2106.08839

zbMATH Keywords

matrix completionnumerical continuationhomotopy methodsRiemannian optimization

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20)

Related Items (1)

Riemannian smoothing gradient type algorithms for nonsmooth optimization problem on compact Riemannian submanifold embedded in Euclidean space

Uses Software

• Manopt
• RTRMC

Cites Work

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• A globally convergent algorithm for computing fixed points of \(C^2\) maps
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• How to conjugate C\(^1\)-close group actions
• Theory of Globally Convergent Probability-One Homotopies for Nonlinear Programming
• Low-Rank Matrix Completion by Riemannian Optimization
• Computing the Fréchet Derivative of the Matrix Logarithm and Estimating the Condition Number
• Introduction to Smooth Manifolds
• Manopt, a Matlab toolbox for optimization on manifolds
• Newton Methods for Nonlinear Problems
• On imbedding and parametric optimization—A concept of a globally convergent algorithm for nonlinear optimization problems
• Iterative Krylov Methods for Large Linear Systems
• Continuous deformation of nonlinear programs
• Riemannian center of mass and mollifier smoothing
• Introduction to Riemannian Manifolds
• A Riemannian BFGS Method Without Differentiated Retraction for Nonconvex Optimization Problems
• Conic Geometric Optimization on the Manifold of Positive Definite Matrices

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