Computing subgradients of convex relaxations for solutions of parametric ordinary differential equations

A novel subgradient evaluation method is proposed for nonsmooth convex relaxations of parametric solutions of ordinary differential equations (ODEs) arising in global dynamic optimization, assuming that the relaxations always lie strictly within interval bounds during integration. We argue that this assumption is reasonable in practice. These subgradients are computed as the unique solution of an auxiliary parametric affine ODE, analogous to …