RPI Math
Current interests lie in integer programming, nonlinear programming, interior point methods, semidefinite programming, portfolio optimization, and stochastic programming.
One thread of research is the investigation of the use of interior point methods to solve integer linear programming problems (ILPs). One way to solve such problems is by employing a cutting plane approach and interior point methods can readily be used in such a method. However, to make the resulting algorithm competitive with the best algorithms for ILPs, several refinements are necessary. This cutting plane method has been implemented to solve matching problems and linear ordering problems with promising results.
Many problems can be formulated as linear programming problems with a very large number of variables. This includes, for example, stochastic programming problems and multicommodity network flow problems. Because of the imposing number of variables, column generation approaches to these problems have been investigated.
Theoretical results regarding the polynomial convergence of interior point column generation and cutting plane methods have been proved.
Semidefinite programming problems arise as relaxations of some integer programming problems and they can be solved using interior point methods.
Another area of research is the development of a parallel interior point branch-and-bound algorithm for the solution of mixed integer nonlinear programming problems.
Click here to see a list of selected recent publications. Click here to see a list of selected sites in optimization and operations research.
I have a bibtex database of optimization references (800K) available online. A searchable version of this bibliography is also available.