Inclusion Certificates and Simultaneous Convexification of Functions

We define the inclusion certificate as a measure that expresses each point in the domain of a collection of functions as a convex combination of other points in the domain. Using inclusion certificates, we extend the convex extensions theory to enable simultaneous convexification of functions. We discuss conditions under which the domain of the functions … Read more

Strong Valid Inequalities for Orthogonal Disjunctions and Bilinear Covering Sets

In this paper, we develop a convexification tool that enables the construction of convex hulls for orthogonal disjunctive sets using convex extensions and disjunctive programming techniques. A distinguishing feature of our technique is that, unlike most applications of disjunctive programming, it does not require the introduction of new variables in the relaxation. We develop and … Read more

Lifting Inequalities: A framework for generating strong cuts in nonlinear programs

In this paper, we propose lifting techniques for generating strong cuts for nonlinear programs that are globally-valid. The theory is geometric and provides intuition into lifting-based cut generation procedures. As a special case, we find short proofs of earlier results on lifting techniques for mixed-integer programs. Using convex extensions, we obtain conditions that allow sequence-independent … Read more