About this site
This site was created as part of the M.Sc. work of Anders Skajaa, a student of applied mathematics at New York University. The thesis entitled "Limited Memory BFGS for Nonsmooth Optimization" investigates the performance of different algorithms for non-smooth optimization. Particular emphasis was put on the LBFGS method with an inexact line search. Work done by Michael L. Overton, New York University and Adrian S. Lewis, Cornell University showed that the standard BFGS method succeeds on certain non-smooth problems when an inexact line search is used. The main question to be answered by the thesis was: Will the LBFGS method succeed on similar problems if the inexact line search is employed? The answer is yes and further the LBFGS succeeds in minimizing non-smooth functions of so many variables that it is infeasible to use the full BFGS. The LBFGS method also compares well to other methods devised for large-scale non-smooth optimization such as this limited memory bundle method, the RedistProx algorithm and this Modified Shor-R algorithm.