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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Veröffentlicht in:	IEEE transactions on information theory Jg. 69; H. 4; S. 2556 - 2602
Hauptverfasser:	Dixit, Rishabh, Gurbuzbalaban, Mert, Bajwa, Waheed U.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York IEEE 01.04.2023 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:	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-Zugang:	Volltext
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