Mathematics and Computer Science Division
Argonne National Laboratory
office: (630) 252-4279
fax: (630) 252-5986
I have also worked on several generalized Newton methods for solving complementarity problems. PATH is based on the normal map formulation of complementarity problems. At each iteration, a linear complementarity problem is solved to calculate a direction. The code is globalized by using the Fischer-Burmeister merit function. The method is enhanced with preprocessing techniques that remove variables and constraints from the given problem, and uncover polyhedral variational inequality structure; nonmontone search criteria; and crashing methods to identify good active sets. Parallel versions of the semismooth methods that I wrote are available in TAO, the Toolkit for Advanced Optimization.
Finally, I have worked on special-purpose algorithms for solving support vector machine and mesh shape-quality optimization problems. The structure of the linear support vector machine problem enabled us to write tailored linear algebra in interior-point and semismooth algorithms so that we can solve extremely large instances (on the order of 60-100 million degrees of freedom).