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We study projection-free methods for constrained Riemannian optimization.
An algorithm for quadratic programming
M. Frank and P. Wolfe · 1956
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Une propriété topologique des sous-ensembles analytiques réels
S. Lojasiewicz · 1963
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Gradient methods for minimizing functionals (in Russian)
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A tight upper bound on the rate of convergence of frank-wolfe algorithm
M. Canon and C. Cullum · 1968
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Convergence theory in nonlinear programming
P. Wolfe · 1970
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An extension of the frank and wolfe method of feasible directions
Charles A. Holloway · 1974
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Finding the point of a polyhedron closest to the origin
B. F. Mitchell, V. F. Dem’yanov, and V. N. Malozemov · 1974
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Riemannian center of mass and mollifier smoothing
H. Karcher · 1977
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Means of positive linear operators
F. Kubo and T. Ando · 1979
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Some comments on Wolfe’s ‘away step’
J. GuéLat and P. Marcotte · 1986
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Convex functions and optimization methods on Riemannian manifolds , volume 297
Constantin Udriste · 1994
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Matrix Analysis
R. Bhatia · 1997
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The geometry of algorithms with orthogonality constraints
A. Edelman, T. A. Arias, and S. T. Smith · 1998
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Diffusion Tensor Imaging: Concepts and Applications
Denis Le Bihan, Jean-François Mangin, Cyril Poupon, Chris A Clark, Sabina Pappata, Nicolas Molko, and Hughes Chabriat · 2001
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Means and averaging in the group of rotations
Maher Moakher · 2002
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Riemannian geometry and matrix geometric means
R. Bhatia and J. Holbrook · 2006
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Riemannian Geometry: A modern introduction , volume 98
Isaac Chavel · 2006
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Helly’s intersection theorem on manifolds of nonpositive curvature
Yuri S Ledyaev, Jay S Treiman, and Qiji J Zhu · 2006
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Positive Definite Matrices
R. Bhatia · 2007
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Essential matrix estimation using Gauss-Newton iterations on a manifold
Uwe Helmke, Knut Hüper, Pei Yean Lee, and John Moore · 2007
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Optimization algorithms on matrix manifolds
P-A Absil, Robert Mahony, and Rodolphe Sepulchre · 2009
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Coresets, sparse greedy approximation, and the frank-wolfe algorithm
Kenneth L. Clarkson · 2010
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Introduction to Optimization
B. T. Polyak · 2010
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Maximizing a submodular set function subject to a matroid constraint
G. Calinescu, C. Chekuri, M. Pál, and J. Vondrák · 2011
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A submodular function minimization algorithm based on the minimum-norm base
S. Fujishige and S. Isotani · 2011
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Riemannian Geometry and Geometric Analysis
J. Jost · 2011
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A survey and comparison of contemporary algorithms for computing the matrix geometric mean
B. Jeuris, R. Vandebril, and B. Vandereycken · 2012
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Matrix power means and the Karcher mean
Yongdo Lim and Miklós Pálfia · 2012
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Non-negative principal component analysis: Message passing algorithms and sharp asymptotics
Andrea Montanari and Emile Richard · 2015
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Conic geometric optimization on the manifold of positive definite matrices
S. Sra and R. Hosseini · 2015
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Complete Dictionary Recovery over the Sphere II: Recovery by Riemannian Trust-region Method
Ju Sun, Qing Qu, and John Wright · 2015
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Global rates of convergence for nonconvex optimization on manifolds
Nicolas Boumal, P-A Absil, and Coralia Cartis · 2016
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Variance-reduced and projection-free stochastic optimization
Elad Hazan and Haipeng Luo · 2016
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Optimization methods on Riemannian manifolds and their application to shape space
Wolfgang Ring and Benedikt Wirth · 2012
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Computing the Karcher mean of symmetric positive definite matrices
D. A. Bini and B. Iannazzo · 2013
Cited alongside, same era.
Revisiting Frank-Wolfe: Projection-free sparse convex optimization
Martin Jaggi · 2013
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Matrix Information Geometry
F. Nielsen and R. Bhatia, editors · 2013
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Geometric optimisation on positive definite matrices for elliptically contoured distributions
Suvrit Sra and Reshad Hosseini · 2013
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Low-rank matrix completion by Riemannian optimization
Bart Vandereycken · 2013
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H. Karimi, J. Nutini, and M. W. Schmidt · 2016
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Convergence rate of Frank-Wolfe for non-convex objectives
S. Lacoste-Julien · 2016
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Operator means of probability measures and generalized karcher equations
Miklós Pálfia · 2016
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Stochastic Frank-Wolfe methods for nonconvex optimization
Sashank J Reddi, Suvrit Sra, Barnabás Póczos, and Alex Smola · 2016
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A riemannian limited-memory bfgs algorithm for computing the matrix geometric mean
Xinru Yuan, Wen Huang, P.-A. Absil, and K.A. Gallivan · 2016
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First-order methods for geodesically convex optimization
H. Zhang and S. Sra · 2016
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Fast stochastic optimization on Riemannian manifolds
H. Zhang, S. Reddi, and S. Sra · 2016
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Iteration-complexity of gradient, subgradient and proximal point methods on Riemannian manifolds
Glaydston C Bento, Orizon P Ferreira, and Jefferson G Melo · 2017
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Manifold optimization for k-means clustering
Timothy Carson, Dustin G. Mixon, and Soledad Villar · 2017
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A Riemannian quasi-Newton method for computing the Karcher mean of symmetric positive definite matrices
Xinru Yuan, Wen Huang, P.-A. Absil, and K. A. Gallivan · 2017
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A majorization-minimization algorithm for computing the Karcher mean of positive definite matrices
T. Zhang · 2017
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On the bures-wasserstein distance between positive definite matrices
Rajendra Bhatia, Tanvi Jain, and Yongdo Lim · 2018
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The riemannian barzilai–borwein method with nonmonotone line search and the matrix geometric mean computation
Bruno Iannazzo and Margherita Porcelli · 2018
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Wasserstein riemannian geometry of positive-definite matrices ?
Luigi Malagò, Luigi Montrucchio, and Giovanni Pistone · 2018
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Simple algorithms for optimization on riemannian manifolds with constraints, 2019
Changshuo Liu and Nicolas Boumal · 2019
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Nonconvex stochastic optimization on manifolds via Riemannian Frank-Wolfe methods
Melanie Weber and Suvrit Sra · 2019
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Complexity of linear minimization and projection on some sets
Cyrille W. Combettes and Sebastian Pokutta · 2021
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