Ph.D. Algorithms, Combinatorics, and Optimization, Carnegie Mellon University, 1996.
Convex Programming, Integer Programming
I mostly work on convex analysis, in particular on semidefinite programming, SDP. SDP is a generalization of linear programming, but its duality theory is more mysterious: we may have unattained optimal values, positive duality gaps, and other curious behaviors. All of these oddities can be traced back to the geometry of a linear image of the cone of symmetric positive semidefinite matrices. Understanding these behaviors can lead to theoretical results and practical preprocessing algorithms. Please see my "selected publications" page, and/or contact me for more information.