(125c) Efficient Linear Underestimators for Dynamic Process Systems
This presentation combines and extends several recent results to obtain an efficient technique for constructing useful affine underestimators for optimization problems with embedded systems of parametric ordinary differential equations (ODEs). Differentiable relaxations are constructed for the ODE right-hand side using a method  developed in the âmultivariate McCormickâ framework . These are then substituted into a description  of efficient ODE relaxations as an auxiliary hybrid discrete/continuous system. It may be shown that various properties of the relaxations of  prevent the discrete behavior of this hybrid system from manifesting, yielding an auxiliary ODE system that describes convex relaxations. Standard adjoint sensitivity analysis techniques may be applied to this system to compute affine underestimators for the overarching optimization problem efficiently using standard ODE solvers. Implications and examples are discussed.
 KA Khan, HAJ Watson, and PI Barton, Differentiable McCormick relaxations, J. Glob. Optim., 67:687-729, 2017.
 JK Scott and PI Barton, Improved relaxations for the parametric solutions of ODEs using differential inequalities, J. Glob. Optim., 57:143-176, 2013.
 A Tsoukalas and A Mitsos, Multivariate McCormick relaxations, J. Glob. Optim., 59:633-662, 2014.