Note: Some of the material referenced below may be copyrighted, and hence is not generally available by clicking on it. That material is posted on the Moodle site for our course.
Outline for a somewhat related course from Fall, 2006
Bibliography
for the 2006 course in PDF format
Outline
for the somewhat related course from Fall, 2003
Bibliography
for the 2003 course in PDF format
Description  Explanation / References / Projects 
A review of basic concepts in linear, convex, and and nonconvex optimization 

A review of basic properties and theorems from interval arithmetic  Excerpts from Classical and Modern Numerical Analysis: Theory, Methods, and Practice. 
The GlobSol software system 
We will focus on the following:
(Pursuit of this topic initially requires access to a linuxbased system with a sufficiently recent installation of the gnu compiler suite. Time will be spent discussing this environment, as necessary.) 
Relaxations in nonconvex optimization, and solution of nonconvex problems without branching in the original space. 
Initial references will be

Handling disconnected images in branch and bound algorithms 
Note: This topic involves constraint propagation, which we will introduce first. An example of constraint propagation is

The following topics will be pursued to the extent they complement and enhance the above topics. 

Parallelization of branch and bound algorithms and MPI. 
A good introduction to use of MPI in parallel computing is Parallel
Scientific Computing in C++ and MPI, George Karniadakis and Robert
M. Kirby II, Cambridge Univ. Press, QA76.58 K37 2003, ISBN 0521817544. Beyond the basics of parallel programming, we may cover parallelization of branch and bound algorithms, following the agenda in 655656 in 20072008. References will be posted on the moodle course. 