Document Type
Article
Department or Administrative Unit
Mathematics
Publication Date
5-8-2015
Abstract
Variational methods find solutions of equations by considering a solution as a critical point of an appropriately chosen function. Local minima and maxima are well-known types of critical points. We explore methods for finding critical points that are neither local maxima or minima, but instead are mountain passes or saddle points. Criteria for the existence of minima or maxima are well known, but those for mountain passes or saddle points are less well known. We give an accessible treatment of some criteria for the existence of such points (including the mountain pass lemma), as well as describe a method that could be used to find such points.
Recommended Citation
Bisgard, J. (2015). Mountain Passes and Saddle Points. SIAM Review, 57(2), 275–292. https://doi.org/10.1137/140963510
Journal
SIAM Review
Rights
© 2015, Society for Industrial and Applied Mathematics.
Comments
This article was originally published in SIAM Review by the Society for Industrial and Applied Mathematics. The full-text article from the publisher can be found here.