Gradient Descent Converges to Minimizers

Differentiable dynamical systems

Stephen Smale · 1967

Earlier work this paper cites.

Newton-type methods for unconstrained and linearly constrained optimization

Philip E Gill and Walter Murray · 1974

Earlier work this paper cites.

Invariant Manifolds

M.W. Hirsch, C.C. Pugh, and M. Shub · 1977

Earlier work this paper cites.

On the use of directions of negative curvature in a modified Newton method

Jorge J Moré and Danny C Sorensen · 1979

Earlier work this paper cites.

Some NP-complete problems in quadratic and nonlinear programming

Katta G Murty and Santosh N Kabadi · 1987

Earlier work this paper cites.

Global stability of dynamical systems

Michael Shub · 1987

Earlier work this paper cites.

Nonconvergence to unstable points in urn models and stochastic approximations

Robin Pemantle · 1990

Earlier work this paper cites.

Trust region methods

Andrew R Conn, Nicholas IM Gould, and Ph L Toint · 2000

Earlier work this paper cites.

Introductory lectures on convex optimization

Yurii Nesterov · 2004

Earlier work this paper cites.

Convergence of the iterates of descent methods for analytic cost functions

Pierre-Antoine Absil, Robert Mahony, and Benjamin Andrews · 2005

Earlier work this paper cites.

Cubic regularization of Newton method and its global performance

Yurii Nesterov and Boris T Polyak · 2006

Cited alongside, same era.

Random fields and geometry

Robert J Adler and Jonathan E Taylor · 2009

Cited alongside, same era.

Matrix completion from a few entries

Raghunandan H. Keshavan, Andrea Montanari, and Sewoong Oh · 2009

Cited alongside, same era.

Proximal alternating minimization and projection methods for nonconvex problems: an approach based on the Kurdyka-Lojasiewicz inequality

Hédy Attouch, Jérôme Bolte, Patrick Redont, and Antoine Soubeyran · 2010

Cited alongside, same era.

Characterizations of Lojasiewicz inequalities: subgradient flows, talweg, convexity

Jérôme Bolte, Aris Daniilidis, Olivier Ley, Laurent Mazet, et al · 2010

Cited alongside, same era.

Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward–backward splitting, and regularized Gauss–Seidel methods

On the saddle point problem for non-convex optimization

Original

Razvan Pascanu, Yann N Dauphin, Surya Ganguli, and Yoshua Bengio · 2014

Later among the works it cites.

Spectral methods meet EM: A provably optimal algorithm for crowdsourcing

Yuchen Zhang, Xi Chen, Denny Zhou, and Michael I Jordan · 2014

Later among the works it cites.

Simple, efficient, and neural algorithms for sparse coding

Sanjeev Arora, Rong Ge, Tengyu Ma, and Ankur Moitra · 2015

Later among the works it cites.

Optimal rates of convergence for noisy sparse phase retrieval via thresholded Wirtinger flow

Original

T Tony Cai, Xiaodong Li, and Zongming Ma · 2015

Later among the works it cites.

Phase retrieval via Wirtinger flow: Theory and algorithms

Emmanuel J Candes, Xiaodong Li, and Mahdi Soltanolkotabi · 2015

Later among the works it cites.