Holden, D. (2018, October 2). Local Minima, Saddle Points, and Plateaus. http://theorangeduck.com/page/local-minima-saddle-points-plateaus. 

University of Michigan - Ann Arbor

For Newton’s method, saddle points clearly constitute a problem. Gradient descent is designed to move “downhill” and is not explicitly designed to seek acritical point. Newton’s method, however, is designed to solve for a point where the gradient is zero. Without appropriate modiﬁcation, it can jump to a saddle point.

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