Computing Mountain Passes

Jorge More' (moremcs.anl.gov)
Todd Munson (tmunsonmcs.anl.gov)

Abstract: We propose the elastic string algorithm for computing mountain passes in finite-dimensional problems. We analyze the convergence properties and numerical performance of this algorithm for benchmark problems in chemistry and discretizations of infinite-dimensional variational problems. We show that any limit point of the elastic string algorithm is a path that crosses a critical point at which the Hessian matrix is not positive definite.

Keywords: mountain passes, saddle points, optimization

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: Argonne Preprint ANL/MCS-P957-0502, Argonne National Laboratory, 2002

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Entry Submitted: 09/19/2002
Entry Accepted: 09/19/2002
Entry Last Modified: 09/19/2002

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