Convex and concave relaxations for the parametric solutions of semi-explicit index-one differential-algebraic equations (Q1949566)

A general system of nonlinear, semi-explicit, index-one differential algebraic equations is considered. The authors develop a numerical method for computing a convex underestimator and a concave overestimator of the parametric solutions of the considered system. The proposed method is automatable and uses a generalization of McCormick's relaxation [\textit{J. K. Scott} et al., J. Glob. Optim. 51, No. 4, 569--606 (2011; Zbl 1232.49033)], and the method of relaxations of the original differential equations [\textit{J. K. Scott} et al., Optim. Control Appl. Methods 34, No. 2, 145--163 (2013; Zbl 1273.93089)].