Speaker: Mohit Tawarmalani
Date: Friday, April 7, 2006
Time: 1:30 to 3:00 pm
Place: 388 Posner Hall
Title: Convex Extensions and Convexification of Nonlinear Sets
Abstract
We develop a theoretical framework of convex extensions that enables building convex envelopes of many nonlinear functions. We then use the framework to analyze inclusion certificates (that guarantee inclusion of a point in the convex hull of a disjunction) and provide insights into various hierarchies of relaxations. We extend the notion of lifting locally valid inequalities to global validity to generate linear and nonlinear inequalities for continuous nonlinear programming. As a consequence, we develop valid inequalities for certain mixed-integer bilinear sets and a procedure for generating convex hulls for certain disjunctive nonlinear sets.
