A framework for generalising the Newton method and other iterative methods from Euclidean space to manifolds

DOI10.1007/s00211-014-0630-4zbMath1307.49025arXiv1207.5087OpenAlexW3105160656MaRDI QIDQ2514241

Jonathan H. Manton

Publication date: 3 February 2015

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1207.5087

zbMATH Keywords

manifoldscost functionminimizationNewton method

Mathematics Subject Classification ID

Newton-type methods (49M15)

Related Items

Newton algorithm on constraint manifolds and the 5-electron Thomson problem ⋮ Kantorovich's theorem on Newton's method under majorant condition in Riemannian manifolds ⋮ On the superlinear convergence of Newton's method on Riemannian manifolds ⋮ Damped Newton's method on Riemannian manifolds ⋮ Second order optimality on orthogonal Stiefel manifolds ⋮ Generalized left-localized Cayley parametrization for optimization with orthogonality constraints ⋮ Iteration-complexity of the subgradient method on Riemannian manifolds with lower bounded curvature ⋮ First Order Methods for Optimization on Riemannian Manifolds ⋮ Iteration-complexity and asymptotic analysis of steepest descent method for multiobjective optimization on Riemannian manifolds ⋮ Gradient Method for Optimization on Riemannian Manifolds with Lower Bounded Curvature

Uses Software

• NewtonLib

Cites Work

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