2011/07/21 by C. H. Jeffrey Pang, Pang, C. H. Jeffrey
Mathematics · Engineering · #Advanced Optimization Algorithms Research #Iterative Methods for Nonlinear Equations #Advanced Numerical Analysis Techniques
paper · pdf · doi:10.48550/arxiv.1107.4287
The problem of computing saddle points is important in certain problems in\nnumerical partial differential equations and computational chemistry, and is\noften solved numerically by a minimization problem over a set of mountain\npasses. We propose an algorithm to find saddle points of mountain pass type to\nfind the bottlenecks of optimal mountain passes. The key step is to minimize\nthe distance between level sets by using quadratic models on affine spaces\nsimilar to the strategy in the conjugate gradient algorithm. We discuss\nparameter choices, convergence results, and how to augment the algorithm to a\npath based method. Finally, we perform numerical experiments to test the\nconvergence of our algorithm.\n