Abstract.
The mountain-pass theorem guarantees the existence of a critical point on a path that connects two points separated by a sufficiently high barrier. We propose the elastic string algorithm for computing mountain passes in finite-dimensional problems and 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.
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This work was supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Advanced Scientific Computing Research, Office of Science, U.S. Department of Energy, under Contract W-31-109-Eng-38.
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Moré, J., Munson, T. Computing mountain passes and transition states. Math. Program., Ser. B 100, 151–182 (2004). https://doi.org/10.1007/s10107-003-0489-0
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DOI: https://doi.org/10.1007/s10107-003-0489-0