SCAIM Seminar: Christoph Ortner

The dimer method is a simple hessian-free algorithm for computing index-1 saddles. In this talk, I will review and analyze a few variants of this algorithm, focusing on 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.