Summary
Several chemical engineering applications involve global optimization of process models in which nonlinear dynamics are encoded as ordinary differential equations (ODEs). In typical deterministic methods for global optimization, crucial lower bounds are generated by minimizing convex relaxations. Hence, we propose a new approach for generating convex relaxations of solutions of parametric ODEs, essentially by combining our recent optimization-based relaxation scheme for ODEs with the powerful Auxiliary Variable Method underlying the state-of-the-art solver BARON. We observe that the optimization problems defining each method can be combined, yielding tight, versatile ODE relaxations that are described by nonsmooth ODEs with convex optimal-value problems embedded.
