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Article Dans Une Revue SIAM Journal on Numerical Analysis Année : 2017

Convergence and Cycling in Walker-type Saddle Search Algorithms

Résumé

Algorithms for computing local minima of smooth objective functions enjoy a mature theory as well as robust and efficient implementations. By comparison, the theory and practice of saddle search is destitute. In this paper we present results for idealized versions of the dimer and gentlest ascent (GAD) saddle search algorithms that show-case the limitations of what is theoretically achievable within the current class of saddle search algorithms: (1) we present an improved estimate on the region of attraction of saddles; and (2) we construct quasi-periodic solutions which indicate that it is impossible to obtain globally convergent variants of dimer and GAD type algorithms.
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Dates et versions

hal-01350514 , version 1 (30-07-2016)

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Antoine Levitt, Christoph Ortner. Convergence and Cycling in Walker-type Saddle Search Algorithms. SIAM Journal on Numerical Analysis, 2017, ⟨10.1137/16M1087199⟩. ⟨hal-01350514⟩
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