Several applications in engineering give rise to optimization problems that must be solved to global optimality, including worst-case uncertainty analysis and modeling of thermodynamic equilibria. Deterministic methods for global optimization proceed by generating successively tighter upper and lower bounds on the unknown optimal objective value, and their convergence rates are typically limited by the quality of these bounds. This presentation describes recent progress in constructing effective bounds on nonconvex systems for this purpose, including automatic generation of differentiable convex underestimators based on pioneering methods by McCormick (1976), and effective incorporation of subgradients. Implementations and examples are discussed.

Kamil Khan is an assistant professor in McMaster University's Department of Chemical Engineering. He received his B.S.E. from Princeton University and his Ph.D. from the Massachusetts Institute of Technology. Before joining McMaster University, he was a Director's Postdoctoral Fellow at the Mathematics and Computer Science Division of the Argonne National Laboratory. His research focuses on optimization and sensitivity analysis of dynamic and nonconvex chemical process models, using techniques such as algorithmic differentiation and convex relaxation.