Convergence and Cycling in Walker-type Saddle Search Algorithms
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Publication:5359495
DOI10.1137/16M1087199zbMATH Open1375.65088arXiv1607.08875MaRDI QIDQ5359495
Author name not available (Why is that?)
Publication date: 25 September 2017
Published in: (Search for Journal in Brave)
Abstract: 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.
Full work available at URL: https://arxiv.org/abs/1607.08875
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