Optimization Online


Behavior of accelerated gradient methods near critical points of nonconvex problems

Michael O'Neill(moneill***at***cs.wisc.edu)
Stephen Wright(swright***at***cs.wisc.edu)

Abstract: We examine the behavior of accelerated gradient methods in smooth nonconvex unconstrained optimization. Each of these methods is typically a linear combination of a gradient direction and the previous step. We show by means of the stable manifold theorem that the heavy-ball method method does not converge to critical points that do not satisfy second-order necessary conditions. We then examine the behavior of two accelerated gradient methods - the heavy-ball method and Nesterov's method - in the vicinity of the saddle point of a nonconvex quadratic function, showing in both cases that the accelerated gradient method can diverge from this point more rapidly than steepest descent.

Keywords: Accelerated Gradient Methods, Nonconvex Optimization

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Citation: Technical Report, University of Wisconsin-Madison, June 2017

Download: [PDF]

Entry Submitted: 06/29/2017
Entry Accepted: 06/29/2017
Entry Last Modified: 06/29/2017

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society