Showing papers by "Jorge J. Moré published in 2004"
TL;DR: The elastic string algorithm is proposed for computing mountain passes in finite-dimensional problems and the convergence properties and numerical performance of this algorithm are analyzed for benchmark problems in chemistry and discretizations of infinite-dimensional variational problems.
Abstract: The mountain-pass theorem guarantees the existence of a critical point on a path that connects two points separated by a sufficiently high barrier We propose the elastic string algorithm for computing mountain passes in finite-dimensional problems and analyze the convergence properties and numerical performance of this algorithm for benchmark problems in chemistry and discretizations of infinite-dimensional variational problems We show that any limit point of the elastic string algorithm is a path that crosses a critical point at which the Hessian matrix is not positive definite
19 citations
30 Aug 2004
TL;DR: This work surveys techniques in the Toolkit for Advanced Optimization for developing scalable algorithms for mesh-based optimization problems on distributed architectures and shows that these techniques, together with mesh sequencing, can produce results that scale with mesh size.
Abstract: We survey techniques in the Toolkit for Advanced Optimization (TAO) for developing scalable algorithms for mesh-based optimization problems on distributed architectures. We discuss the distribution of the mesh, the computation of the gradient and the Hessian matrix, and the use of preconditioners. We show that these techniques, together with mesh sequencing, can produce results that scale with mesh size.
6 citations