Title: Computing Transition States and Mountain-Passes
Presentation Slides

The mountain-pass theorem is a remarkable result that forms the basis for the calculation of transition states in biology and chemistry. The mountain-pass theorem is also a fundamental tool in nonlinear analysis where it is used to prove existence results for variational problems in infinite-dimensional dynamical systems. In this talk we describe the background for the mountain-pass theorem, and propose an algorithm - the elastic string algorithm - for the computation of transition states in finite-dimensional problems.
The background needed for this presentation is minimal since we want to emphasize the main ideas and minimize the details. We provide an overview of the convergence properties of the elastic string algorithm, and show, via numerical results, that any limit point of the algorithm is a path that crosses a critical point at which the Hessian matrix is not positive definite. The behavior of the elastic string algorithm will be examined via computational results for benchmark problems in chemistry and infinite-dimensional variational problems.
Short Bio:
Jorge J. Moré is Distinguished Senior Computer Scientist in the Mathematics and Computer Science Division at Argonne National Laboratory. His research interests center on developing algorithms and software for large-scale optimization problems with emphasis on optimization environments and high-performance architectures. Dr. Moré is currently a major developer in the NEOS and TAO projects, and serves on a number of boards, including the SIAM Journal on Optimization, Mathematical Programming, SIAM Series on Software, Environments, Tools, and the Wilkinson Prize for Numerical Software. He is also co-Director of the Optimization Technology Center, a joint research organization of Argonne and Northwestern University.