Control parametrization: a unified approach to optimal control problems with general constraints
Automatica (Journal of IFAC)
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. IV: optimization and nonlinear equations
Deterministic Global Optimization in Nonlinear Optimal Control Problems
Journal of Global Optimization
A Rigorous Global Optimization Algorithm for Problems with Ordinary Differential Equations
Journal of Global Optimization
A review of recent advances in global optimization
Journal of Global Optimization
Generalized McCormick relaxations
Journal of Global Optimization
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A deterministic spatial branch and bound global optimization algorithm for problems with ordinary differential equations in the constraints has been developed by Papamichail and Adjiman [A rigorous global optimization algorithm for problems with ordinary differential equations. J. Glob. Optim. 24, 1---33]. In this work, it is shown that the algorithm is guaranteed to converge to the global solution. The proof is based on showing that the selection operation is bound improving and that the bounding operation is consistent. In particular, it is shown that the convex relaxation techniques used in the algorithm for the treatment of the dynamic information ensure bound improvement and consistency are achieved.