Research InterestsMy research interests lie in optimization theory and application of optimization techniques to problems in arising in financial and engineering models. On the theory side, I work on the development, analysis, and implementation of interior-point methods for the solution of convex optimization problems. In particular, I studied potential-reduction methods for linear optimization problems and have been collaborating with Mike Todd and Kim Toh on development of algorithms and software for semidefinite programming and second-order cone programming problems. SDPT3 is the product of this collaboration.
My work on the application of optimization techniques focuses on financial and chemical engineering problems. In recent projects, I studied a new method for fast and reliable computation of the optimal risky portfolios and worked on the development of a new algorithm for robust solution of asset allocation problems when the statistical input parameters are unreliable. Current projects include multivariate model fitting problems and risk management using coherent risk measures.
My ongoing research is funded by a CAREER grant from the NSF (CCR-9875559). You can see an abstract of the related proposal.