# Todd S. Munson

Mathematics and Computer Science Division

Argonne National Laboratory

office: (630) 252-4279

fax: (630) 252-5986

e-mail:[email protected]

## Research

My primary research focus is algorithms and applications of optimization
and complementarity.
Most recently I have been working on utilizing constrained nonlinear
optimization techniques to compute mountain passes, critical points where
the Hessian has exactly one negative eigenvalue. Mountain passes are of
interest, for example, in computational chemistry where they correspond to
transition states for chemical reactions. I have also been working
with on an application of optimization to the r-refinement problem,
a large nonlinear, nonconvex optimization problem that can cause grief
for many general-purpose methods.
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).

[email protected]