Boundary Conditions for Linear Exit Time Gradient Trajectories Around Saddle Points: Analysis and Algorithm

Gradient-related first-order methods have become the workhorse of large-scale numerical optimization problems. Many of these problems involve nonconvex objective functions with multiple saddle points, which necessitates an understanding of the behavior of discrete trajectories of first-order methods...

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Bibliographic Details
Published in:	IEEE transactions on information theory Vol. 69; no. 4; pp. 2556 - 2602
Main Authors:	Dixit, Rishabh, Gurbuzbalaban, Mert, Bajwa, Waheed U.
Format:	Journal Article
Language:	English
Published:	New York IEEE 01.04.2023 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Algorithms Boundary conditions Convergence Geometry gradient descent linear-time exit Morse function Neighborhoods nonconvex optimization Optimization Perturbation methods saddle escape Saddle points strict-saddle property Sufficient conditions Trajectory Trajectory analysis
ISSN:	0018-9448, 1557-9654
Online Access:	Get full text
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