TY - JOUR A1 - Hante, Falk M. A1 - Schmidt, Martin T1 - Convergence of Finite-Dimensional Approximations for Mixed-Integer Optimization with Differential Equations JF - Control and Cybernetics N2 - We consider a direct approach to solve mixed-integer nonlinear optimization problems with constraints depending on initial and terminal conditions of an ordinary differential equation. In order to obtain a finite-dimensional problem, the dynamics are approximated using discretization methods. In the framework of general one-step methods, we provide sufficient conditions for the convergence of this approach in the sense of the corresponding optimal values. The results are obtained by considering the discretized problem as a parametric mixed-integer nonlinear optimization problem in finite dimensions, where the maximum step size for discretizing the dynamics is the parameter. In this setting, we prove the continuity of the optimal value function under a stability assumption for the integer feasible set and second-order conditions from nonlinear optimization. We address the necessity of the conditions on the example of pipe sizing problems for gas networks. KW - Optimization with differential equations KW - Optimal value function KW - Lipschitz continuity KW - Parametric optimization KW - Mixed-integer nonlinear programming Y1 - 2018 ER -