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A dimer-type saddle search algorithm with preconditioning and linesearch


Authors: N. Gould, C. Ortner and D. Packwood
Journal: Math. Comp. 85 (2016), 2939-2966
MSC (2010): Primary 65K99, 90C06, 65Z05
Published electronically: March 22, 2016
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Abstract | References | Similar Articles | Additional Information

Abstract: The dimer method is a Hessian-free algorithm for computing saddle points. We augment the method with a linesearch mechanism for automatic step size selection as well as preconditioning capabilities. We prove local linear convergence. A series of numerical tests demonstrate significant performance gains.


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Additional Information

N. Gould
Affiliation: Scientific Computing Department, STFC-Rutherford Appleton Laboratory, Chilton, OX11 0QX, United Kingdom
Email: nick.gould@stfc.ac.uk

C. Ortner
Affiliation: Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, United Kingdom
Email: christoph.ortner@warwick.ac.uk

D. Packwood
Affiliation: Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, United Kingdom
Email: d.packwood@warwick.ac.uk

DOI: https://doi.org/10.1090/mcom/3096
Keywords: Saddle search, perconditioning, convergence, dimer method
Received by editor(s): July 30, 2014
Received by editor(s) in revised form: April 28, 2015
Published electronically: March 22, 2016
Additional Notes: This work was supported in part by EPSRC grants EP/J021377/1 and EP/J022055/1.
Article copyright: © Copyright 2016 American Mathematical Society