Towards global bilevel dynamic optimization
Journal of Global Optimization
Discretize-then-relax approach for convex/concave relaxations of the solutions of parametric ODEs
Applied Numerical Mathematics
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Open loop optimal control problems with linear hybrid (discrete/continuous) systems embedded are often approximated as dynamic optimization problems. We propose a deterministic global optimization algorithm for linear hybrid systems with varying transition times. First, the control parametrization enhancing transform is used to transform the problem from a linear hybrid system with scaled discontinuities and varying transition times into a nonlinear one with stationary discontinuities and fixed transition times. Next, a theory is developed for constructing convex relaxations of arbitrary Bolza-type functionals subject to the transformed hybrid system. Finally, the convex relaxations are utilized in a branch-and-bound framework to obtain the solution to $\varepsilon$ global optimality within a finite number of iterations.