Fetching the paper…
Reading the bibliography…
In this paper, we consider optimization problems over closed embedded submanifolds of $\mathbb{R}^n$, which are defined by the constraints $c(x) = 0$.
Methods of conjugate gradients for solving linear systems
Magnus R Hestenes and Eduard Stiefel · 1952
Earlier work this paper cites.
Sur le probleme de la division
Stanisław Łojasiewicz · 1961
Earlier work this paper cites.
Une propriété topologique des sous-ensembles analytiques réels
Stanislaw Lojasiewicz · 1963
Earlier work this paper cites.
A method for nonlinear constraints in minimization problems
Michael JD Powell · 1969
Earlier work this paper cites.
A class of methods for nonlinear programming with termination and convergence properties
Roger Fletcher · 1970
Earlier work this paper cites.
Solving sparse symmetric generalized eigenvalue problems without factorization
David S Scott · 1981
Earlier work this paper cites.
Towards an efficient sparsity exploiting Newton method for minimization
Philippe Toint · 1981
Earlier work this paper cites.
The conjugate gradient method and trust regions in large scale optimization
Trond Steihaug · 1983
Earlier work this paper cites.
Newton-type minimization via the Lanczos method
Stephen G Nash · 1984
Earlier work this paper cites.
An exact penalty function method with global convergence properties for nonlinear programming problems
Gianni Di Pillo and Luigi Grippo · 1986
Earlier work this paper cites.
A nonmonotone line search technique for Newton’s method
Luigi Grippo, Francesco Lampariello, and Stephano Lucidi · 1986
Earlier work this paper cites.
A limited memory algorithm for bound constrained optimization
Richard H Byrd, Peihuang Lu, Jorge Nocedal, and Ciyou Zhu · 1995
Earlier work this paper cites.
Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization
Ciyou Zhu, Richard H Byrd, Peihuang Lu, and Jorge Nocedal · 1997
Earlier work this paper cites.
The geometry of algorithms with orthogonality constraints
Alan Edelman, Tomás A Arias, and Steven T Smith · 1998
Earlier work this paper cites.
Solving the trust-region subproblem using the Lanczos method
Nicholas IM Gould, Stefano Lucidi, Massimo Roma, and Philippe L Toint · 1999
Earlier work this paper cites.
Trust region methods
Andrew R Conn, Nicholas IM Gould, and Philippe L Toint · 2000
Earlier work this paper cites.
Nonlinear programming without a penalty function
Roger Fletcher and Sven Leyffer · 2002
Earlier work this paper cites.
Cubic regularization of Newton method and its global performance
Yurii Nesterov and Boris T Polyak · 2006
Earlier work this paper cites.
Numerical optimization
Jorge Nocedal and Stephen Wright · 2006
Earlier work this paper cites.
Trust-region methods on Riemannian manifolds
P-A Absil, Christopher G Baker, and Kyle A Gallivan · 2007
Earlier work this paper cites.
Steepest descent algorithms for optimization under unitary matrix constraint
Traian E Abrudan, Jan Eriksson, and Visa Koivunen · 2008
Earlier work this paper cites.
Conjugate gradient algorithm for optimization under unitary matrix constraint
Traian Abrudan, Jan Eriksson, and Visa Koivunen · 2009
Earlier work this paper cites.
Optimization algorithms on matrix manifolds
P-A Absil, Robert Mahony, and Rodolphe Sepulchre · 2009
Earlier work this paper cites.
An inexact interior point method for l 1-regularized sparse covariance selection
Lu Li and Kim-Chuan Toh · 2010
Earlier work this paper cites.
Riemannian BFGS algorithm with applications
Chunhong Qi, Kyle A Gallivan, and P-A Absil · 2010
Earlier work this paper cites.
Critical landscape topology for optimization on the symplectic group
R-B Wu, Raj Chakrabarti, and Herschel Rabitz · 2010
Earlier work this paper cites.
Remark on “algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound constrained optimization”
José Luis Morales and Jorge Nocedal · 2011
Cited alongside, same era.
An adaptive cubic regularization algorithm for nonconvex optimization with convex constraints and its function-evaluation complexity
Coralia Cartis, Nicholas IM Gould, and Ph L Toint · 2012
Cited alongside, same era.
Complexity bounds for second-order optimality in unconstrained optimization
Coralia Cartis, Nicholas IM Gould, and Ph L Toint · 2012
Cited alongside, same era.
Matrix computations
Gene H Golub and Charles F Van Loan · 2013
Cited alongside, same era.
A feasible method for optimization with orthogonality constraints
Zaiwen Wen and Wotao Yin · 2013
Cited alongside, same era.
Minimization principles and computation for the generalized linear response eigenvalue problem
Learning continuous hierarchies in the Lorentz model of hyperbolic geometry
Maximillian Nickel and Douwe Kiela · 2018
Later among the works it cites.
Towards Riemannian accelerated gradient methods
Hongyi Zhang and Suvrit Sra · 2018
Later among the works it cites.
R-spider: A fast Riemannian stochastic optimization algorithm with curvature independent rate
Jingzhao Zhang, Hongyi Zhang, and Suvrit Sra · 2018
Later among the works it cites.
Efficiently escaping saddle points on manifolds
Chris Criscitiello and Nicolas Boumal · 2019
Later among the works it cites.
Parallelizable algorithms for optimization problems with orthogonality constraints
Bin Gao, Xin Liu, and Ya-xiang Yuan · 2019
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Zhaojun Bai and Ren-Cang Li · 2014
Cited alongside, same era.
Proximal alternating linearized minimization for nonconvex and nonsmooth problems
Jérôme Bolte, Shoham Sabach, and Marc Teboulle · 2014
Cited alongside, same era.
Manopt, a matlab toolbox for optimization on manifolds
Nicolas Boumal, Bamdev Mishra, P-A Absil, and Rodolphe Sepulchre · 2014
Cited alongside, same era.
ipiano: Inertial proximal algorithm for nonconvex optimization
Peter Ochs, Yunjin Chen, Thomas Brox, and Thomas Pock · 2014
Cited alongside, same era.
Scalable nonlinear programming via exact differentiable penalty functions and trust-region Newton methods
Victor M Zavala and Mihai Anitescu · 2014
Cited alongside, same era.
Low-rank matrix completion via preconditioned optimization on the grassmann manifold
Nicolas Boumal and P-A Absil · 2015
Cited alongside, same era.
Escaping from saddle points–online stochastic gradient for tensor decomposition
Rong Ge, Furong Huang, Chi Jin, and Yang Yuan · 2015
Cited alongside, same era.
First-order methods almost always avoid strict saddle points
Jason D Lee, Ioannis Panageas, Georgios Piliouras, Max Simchowitz, Michael I Jordan, and Benjamin Recht · 2019
Later among the works it cites.
Stochastic gradient descent for nonconvex learning without bounded gradient assumptions
Yunwen Lei, Ting Hu, Guiying Li, and Ke Tang · 2019
Later among the works it cites.
Accelerated optimization with orthogonality constraints
Jonathan W Siegel · 2019
Later among the works it cites.
An introduction to optimization on smooth manifolds
Nicolas Boumal · 2020
Later among the works it cites.
An accelerated first-order method for non-convex optimization on manifolds
Chris Criscitiello and Nicolas Boumal · 2020
Later among the works it cites.
Implementing a smooth exact penalty function for equality-constrained nonlinear optimization
Ron Estrin, Michael P Friedlander, Dominique Orban, and Michael A Saunders · 2020
Later among the works it cites.
Array programming with numpy
Charles R Harris, K Jarrod Millman, Stéfan J van der Walt, Ralf Gommers, Pauli Virtanen, David Cournapeau, Eric Wieser, Julian Taylor, Sebastian Berg, Nathaniel J Smith, et al · 2020
Later among the works it cites.
A brief introduction to manifold optimization
Jiang Hu, Xin Liu, Zai-Wen Wen, and Ya-Xiang Yuan · 2020
Later among the works it cites.
An efficient orthonormalization-free approach for sparse dictionary learning and dual principal component pursuit
Xiaoyin Hu and Xin Liu · 2020
Later among the works it cites.
Geoopt: Riemannian optimization in pytorch
Max Kochurov, Rasul Karimov, and Serge Kozlukov · 2020
Later among the works it cites.
Scipy 1.0: fundamental algorithms for scientific computing in python
Pauli Virtanen, Ralf Gommers, Travis E Oliphant, Matt Haberland, Tyler Reddy, David Cournapeau, Evgeni Burovski, Pearu Peterson, Warren Weckesser, Jonathan Bright, et al · 2020
Later among the works it cites.
Multipliers correction methods for optimization problems over the Stiefel manifold
Lei Wang, Bin Gao, and Xin Liu · 2020
Later among the works it cites.
Cubic regularization with momentum for nonconvex optimization
Zhe Wang, Yi Zhou, Yingbin Liang, and Guanghui Lan · 2020
Later among the works it cites.
A class of smooth exact penalty function methods for optimization problems with orthogonality constraints
Nachuan Xiao, Xin Liu, and Ya-xiang Yuan · 2020
Later among the works it cites.
Riemannian cubics in quadratic matrix Lie groups
Erchuan Zhang and Lyle Noakes · 2020
Later among the works it cites.
Riemannian optimization on the symplectic Stiefel manifold
Bin Gao, Nguyen Thanh Son, P-A Absil, and Tatjana Stykel · 2021
Later among the works it cites.
Symplectic eigenvalue problem via trace minimization and Riemannian optimization
Nguyen Thanh Son, P-A Absil, Bin Gao, and Tatjana Stykel · 2021
Later among the works it cites.
Solving optimization problems over the Stiefel manifold by smooth exact penalty function
Nachuan Xiao and Xin Liu · 2021
Later among the works it cites.
Exact penalty function for ℓ 2 , 1 \ell_{2,1} norm minimization over the Stiefel manifold
Nachuan Xiao, Xin Liu, and Ya-xiang Yuan · 2021
Later among the works it cites.
Nachuan Xiao, Xin Liu, and Ya-xiang Yuan · 2021
Later among the works it cites.