A Riemannian BFGS Method for Nonconvex Optimization Problems

DOI10.1007/978-3-319-39929-4_60zbMath1352.65153OpenAlexW2465585463MaRDI QIDQ3179709

Wen Huang, Kyle A. Gallivan, Pierre-Antoine Absil

Publication date: 19 December 2016

Published in: Lecture Notes in Computational Science and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-39929-4_60

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05)

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Cites Work

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• Minimizing a differentiable function over a differential manifold
• A perfect example for the BFGS method
• A Riemannian symmetric rank-one trust-region method
• On the Global Convergence of the BFGS Method for Nonconvex Unconstrained Optimization Problems
• Optimization Methods on Riemannian Manifolds and Their Application to Shape Space
• A Broyden Class of Quasi-Newton Methods for Riemannian Optimization
• A Tool for the Analysis of Quasi-Newton Methods with Application to Unconstrained Minimization
• Quasi-Newton Methods on Grassmannians and Multilinear Approximations of Tensors
• A modified BFGS method and its global convergence in nonconvex minimization

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