Optimization On Manifolds: Methods And Applications

No abstract is available for this paper.

• Publication year

  2010

• Venue

  Unknown venue

• Publication date

  2010-12-01

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1007/978-3-642-12598-0_12
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• A Gradient-Descent Method for Curve Fitting on Riemannian Manifolds

  2011cited by this paper
• Best Low Multilinear Rank Approximation of Higher-Order Tensors, Based on the Riemannian Trust-Region Scheme

  2011cited by this paper
• Identification method for time-varying ARX models

  2010cited by this paper
• A Riemannian Optimization Approach for Computing Low-Rank Solutions of Lyapunov Equations

  2010cited by this paper
• Riemannian BFGS Algorithm with Applications

  2010cited by this paper
• On the best low multilinear rank approximation of higher-order tensors

  2010cited by this paper
• Recent Advances in Optimization and its Applications in Engineering

  2010cited by this paper
• Soft Dimension Reduction for ICA by Joint Diagonalization on the Stiefel Manifold

  2009cited by this paper
• Identification method for time-varying ARX models (abstract)

  2009cited by this paper
• The Riemannian BFGS algorithm with applications (abstract)

  2009cited by this paper
• Representing the space of linear programs as the Grassmann manifold

  2009cited by this paper
• Geodesic finite elements for Cosserat rods

  2009cited by this paper
• Optimization algorithms on matrix manifolds

  2009influential reference
• A Newton-Grassmann Method for Computing the Best Multilinear Rank-(r1, r2, r3) Approximation of a Tensor

  2009cited by this paper
• All roads lead to Newton: Feasible second-order methods for equality-constrained optimization ∗

  2009cited by this paper
• Embedded geometry of the set of symmetric positive semidefinite matrices of fixed rank

  2009cited by this paper
• Intrinsic mean shift for clustering on Stiefel and Grassmann manifolds

  2009cited by this paper
• Monotone vector fields and the proximal point algorithm on Hadamard manifolds

  2009cited by this paper
• Numerical Representations of a Universal Subspace Flow for Linear Programs

  2008cited by this paper
• Statistical analysis on Stiefel and Grassmann manifolds with applications in computer vision

  2008cited by this paper
• Primal Central Paths and Riemannian Distances for Convex Sets

  2008cited by this paper
• RIEMANNIAN MANIFOLD TRUST-REGION METHODS WITH APPLICATIONS TO EIGENPROBLEMS

  2008cited by this paper
• An implicit trust-region method on Riemannian manifolds

  2008cited by this paper
• Natural Conjugate Gradient on Complex Flag Manifolds for Complex Independent Subspace Analysis

  2008cited by this paper
• Riemannian Metric and Geometric Mean for Positive Semidefinite Matrices of Fixed Rank

  2008cited by this paper
• Best multilinear rank approximation of tensors with quasi-Newton methods on Grassmannians

  2008cited by this paper
• A Novel Representation for Riemannian Analysis of Elastic Curves in Rn

  2007cited by this paper
• Newton's method on Gra{\ss}mann manifolds

  2007cited by this paper
• Trust-Region Methods on Riemannian Manifolds

  2007cited by this paper
• Essential Matrix Estimation Using Gauss-Newton Iterations on a Manifold

  2007cited by this paper
• Bayesian Filtering on the Stiefel Manifold

  2007cited by this paper
• Riemannian subspace tracking algorithms on Grassmann manifolds

  2007cited by this paper
• A centroid (Karcher mean) approach to the joint approximate diagonalisation problem: The real symmetric case

  2006cited by this paper
• Local Convergence Properties of Fastica and Some Generalisations

  2006cited by this paper
• Geometrical interpretation of the predictor-corrector type algorithms in structured optimization problems

  2006cited by this paper
• Geodesics Between 3D Closed Curves Using Path-Straightening

  2006cited by this paper
• Joint Diagonalization on the Oblique Manifold for Independent Component Analysis

  2006cited by this paper
• An Implicit Riemannian Trust-Region Method for the Symmetric Generalized Eigenproblem

  2006cited by this paper
• Newton-Like Methods for Nonparametric Independent Component Analysis

  2006cited by this paper
• A truncated-CG style method for symmetric generalized eigenvalue problems

  2006cited by this paper
• Newton methods for nonsmooth convex minimization: connections among -Lagrangian, Riemannian Newton and SQP methods

  2005cited by this paper
• Tools for application-driven linear dimension reduction

  2005cited by this paper
• Learning algorithms utilizing quasi-geodesic flows on the Stiefel manifold

  2005cited by this paper
• Geometrical methods for non-negative ICA: Manifolds, Lie groups and toral subalgebras

  2005cited by this paper
• Adaptive Model Trust Region Methods for Generalized Eigenvalue Problems

  2005cited by this paper
• Bayesian and geometric subspace tracking

  2004cited by this paper
• Efficient Rank Reduction of Correlation Matrices

  2004cited by this paper
• Some Gradient Based Joint Diagonalization Methods for ICA

  2004cited by this paper
• Optimal linear representations of images for object recognition

  2004cited by this paper
• Riemannian Geometry of Grassmann Manifolds with a View on Algorithmic Computation

  2004cited by this paper
• Analysis of planar shapes using geodesic paths on shape spaces

  2004cited by this paper
• Cubically Convergent Iterations for Invariant Subspace Computation

  2004cited by this paper
• The Riccati algorithm for eigenvalues and invariant subspaces of matrices with inexpensive action

  2003cited by this paper
• On the Curvature of the Central Path of Linear Programming Theory

  2003cited by this paper
• The Geometry of the Newton Method on Non-Compact Lie Groups

  2002cited by this paper
• Active Sets, Nonsmoothness, and Sensitivity

  2002cited by this paper
• The multimode Procrustes problem

  2002cited by this paper
• Joint diagonalization of correlation matrices by using gradient methods with application to blind signal separation

  2002cited by this paper
• Algorithms on the Stiefel manifold for joint diagonalisation

  2002cited by this paper
• Newton's method on Riemannian manifolds and a geometric model for the human spine

  2002cited by this paper
• Controllability of the QR Algorithm on Hessenberg Flags

  2002cited by this paper
• Optimization algorithms exploiting unitary constraints

  2002cited by this paper
• Unified stabilization approach to principal and minor components extraction algorithms

  2001cited by this paper
• Optimization Criteria and Geometric Algorithms for Motion and Structure Estimation

  2001cited by this paper
• Computing Lyapunov exponents on a Stiefel manifold

  2001cited by this paper
• On VU-theory for Functions with Primal-Dual Gradient Structure

  2000influential reference
• Nonholonomic Orthogonal Learning Algorithms for Blind Source Separation

  2000cited by this paper
• Joint Approximate Diagonalization of Positive Definite Hermitian Matrices

  2000cited by this paper
• Self-stabilized gradient algorithms for blind source separation with orthogonality constraints

  2000cited by this paper
• Templates for the Solution of Algebraic Eigenvalue Problems

  2000cited by this paper
• A Grassmann-Rayleigh quotient iteration for computing invariant subspaces

  2000cited by this paper
• Adaptive Eigenvalue Computations Using Newton's Method on the Grassmann Manifold

  1999cited by this paper
• A Procrustes problem on the Stiefel manifold

  1999cited by this paper
• The Geometry of Algorithms with Orthogonality Constraints

  1998cited by this paper
• THE U -LAGRANGIAN OF A CONVEX FUNCTION

  1996cited by this paper
• Optimization and Dynamical Systems

  1994cited by this paper
• The geometry of matrix eigenvalue methods

  1986cited by this paper
• Introduction to linear and nonlinear programming

  1973cited by this paper
• Foundations of Differentiable Manifolds and Lie Groups

  1971cited by this paper
• Methods of conjugate gradients for solving linear systems

  1952cited by this paper
• Richtungsfelder und Fernparallelismus in n-dimensionalen Mannigfaltigkeiten

  1935cited by this paper
• Wörterbuch zum Rig-Veda

  year unknowncited by this paper

• Waveform Design for Clutter Suppression With Adaptive Spectrum and Sidelobe via Riemannian Manifold Optimization

  2026cites this paper
• Fast(er) Robust Point Cloud Alignment Using Lie Algebra

  2025cites this paper
• Robust Optimization for Movable Antenna-Aided Cell-Free ISAC With Time Synchronization Errors

  2025cites this paper
• Meta-Reinforcement Learning Optimization for Movable Antenna-aided Full-Duplex CF-DFRC Systems with Carrier Frequency Offset

  2025influential citation
• A Riemannian Optimization Perspective of the Gauss-Newton Method for Feedforward Neural Networks

  2024cites this paper
• Exploratory Bi-factor Analysis with Multiple General Factors

  2023influential citation
• Quartic Riemannian Adaptive Regularization With Cubics for Radar Waveform Design

  2023cites this paper
• A Survey of Geometric Optimization for Deep Learning: From Euclidean Space to Riemannian Manifold

  2023cites this paper
• Extrinsic Bayesian Optimizations on Manifolds

  2022cites this paper
• Manifold Adversarial Learning for Cross-domain 3D Shape Representation

  2022cites this paper
• Data analysis using Riemannian geometry and applications to chemical engineering

  2022cites this paper
• Curvature and Torsion estimation of 3D functional data: A geometric approach to build the mean shape under the Frenet Serret framework

  2022cites this paper
• Towards understanding deep learning with the natural clustering prior

  2022cites this paper
• A Sparse Oblique-Manifold Nonnegative Matrix Factorization for Hyperspectral Unmixing

  2022cites this paper
• Clarke Subdifferential, Pareto-Clarke Critical Points and Descent Directions to Multiobjective Optimization on Hadamard Manifolds

  2021cites this paper
• A Riemannian Primal-dual Algorithm Based on Proximal Operator and its Application in Metric Learning

  2020cites this paper
• Geometry of variational methods: dynamics of closed quantum systems

  2020cites this paper
• Towards Optimization Techniques on Diffeological Spaces by Generalizing Riemannian Concepts

  2020cites this paper
• Accelerated algorithms for convex and non-convex optimization on manifolds

  2020cites this paper
• Layer rotation: a surprisingly simple indicator of generalization in deep networks?

  2019cites this paper
• Multiview Transfer Learning and Multitask Learning

  2019cites this paper
• Efficiently escaping saddle points on manifolds

  2019cites this paper
• Mean curvature and mean shape for multivariate functional data under Frenet-Serret framework.

  2019cites this paper
• Incremental Visual Tracking with l 1 Norm Approximation and Grassmann Update

  2018cites this paper
• On layer-level control of DNN training and its impact on generalization

  2018cites this paper
• A Variational Approach to Registration with Local Exponential Coordinates

  2018cites this paper
• Proximal Point Methods for Lipschitz Functions on Hadamard Manifolds: Scalar and Vectorial Cases

  2018cites this paper
• Archetypal Analysis: Mining Weather and Climate Extremes

  2017cites this paper
• A New Approach to the Proximal Point Method: Convergence on General Riemannian Manifolds

  2016cites this paper
• Differential geometric representations and algorithms for some pattern recognition and computer vision problems

  2014cites this paper
• Left-Invariant Riemannian Geodesics on Spatial Transformation Groups

  2014cites this paper
• Spatiotemporal Alignment of Visual Signals on a Special Manifold

  2013cites this paper
• Piecewise rigid curve deformation via a Finsler steepest descent

  2013cites this paper
• Finsler Steepest Descent with Applications to Piecewise-regular Curve Evolution

  2013cites this paper
• Projection-like Retractions on Matrix Manifolds

  2012cites this paper
• Optimization Methods on Riemannian Manifolds and Their Application to Shape Space

  2012cites this paper
• Ring Theory, Group Actions, Evolutionary Algorithms, and Global Optimization

  2012cites this paper
• Segmentation, Recognition, and Alignment of Collaborative Group motion

  2011cites this paper
• Minimum Mean Square Distance Estimation of a Subspace

  2011cites this paper
• Riemannian BFGS Algorithm with Applications

  2010cites this paper
• An Efficient BFGS Algorithm for Riemannian Optimization

  2010cites this paper