Convex and Concave Relaxations for the Parametric Solutions of Semi‐explicit Index‐One Differential‐Algebraic Equations

A method is presented for computing convex and concave relaxations of the parametric solutions of nonlinear, semi‐explicit, index‐one differential‐algebraic equations (DAEs). These relaxations are central to the development of a deterministic global optimization algorithm for problems with DAEs embedded. The proposed method uses relaxations of the DAE equations to derive an auxiliary system of DAEs, the solutions of which are proven to provide the desired relaxations. The entire procedure is fully automatable.