optimization with differential equations

Convergence of Finite-Dimensional Approximations for Mixed-Integer Optimization with Differential Equations

Published: 2018/12/05, Updated: 2019/12/16

(Mixed) Integer Nonlinear Programming, Nonlinear Optimization, Systems governed by Differential Equations Optimization lipschitz continuity, mixed-integer nonlinear programming, optimal value function, optimization with differential equations, parametric optimization

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 … Read more

Towards Simulation Based Mixed-Integer Optimization with Differential Equations

Published: 2016/07/14, Updated: 2017/09/25

(Mixed) Integer Nonlinear Programming, Applications - Science and Engineering, Systems governed by Differential Equations Optimization decomposition, gas transport networks, mixed-integer programming, optimization with differential equations, simulation-based optimization

We propose a decomposition based method for solving mixed-integer nonlinear optimization problems with “black-box” nonlinearities, where the latter, e.g., may arise due to differential equations or expensive simulation runs. The method alternatingly solves a mixed-integer linear master problem and a separation problem for iteratively refining the mixed-integer linear relaxation of the nonlinearity. We prove that … Read more