| Christoph Ortner, Mathematics Institute, University of Warwick |
| Title: The Dimer Method for Saddle Point Computations |
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Abstract:The dimer method is a simple hessian-free algorithm for computing index-1 saddles. I will review this algorithm and describe some improvements to its efficiency, in particular adding preconditioning capabilities and line-search based on a local merit function. I will demonstrate the efficiency of the new variant on a range of applications from academic toy problems, an atomistic problem and a PDE problem. Despite these new improvements, we can currently give no global convergence guarantee. Indeed, we can construct counterexamples to global convergence. I will conclude my talk by explaining some of the difficulties we encountered and posing a challenge for the optimisation community. |