How to fight the wrapping effect
Proceedings of the International Symposium on interval mathematics on Interval mathematics 1985
Control parametrization: a unified approach to optimal control problems with general constraints
Automatica (Journal of IFAC)
Computer simulation of liquids
Computer simulation of liquids
Global optimization approach to nonlinear optimal control
Journal of Optimization Theory and Applications
SIAM Journal on Scientific Computing
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
Deterministic Global Optimization: Theory, Methods and (NONCONVEX OPTIMIZATION AND ITS APPLICATIONS Volume 37) (Nonconvex Optimization and Its Applications)
Journal of Global Optimization
Global Optimization with Nonlinear Ordinary Differential Equations
Journal of Global Optimization
A review of recent advances in global optimization
Journal of Global Optimization
Towards global bilevel dynamic optimization
Journal of Global Optimization
Fluid analysis of energy consumption using rewards in massively parallel markov models
Proceedings of the 2nd ACM/SPEC International Conference on Performance engineering
Discretize-then-relax approach for convex/concave relaxations of the solutions of parametric ODEs
Applied Numerical Mathematics
Generalized McCormick relaxations
Journal of Global Optimization
Optimal switching control of a fed-batch fermentation process
Journal of Global Optimization
Improved relaxations for the parametric solutions of ODEs using differential inequalities
Journal of Global Optimization
Optimal control of switched systems and its parallel optimization algorithm
Journal of Computational and Applied Mathematics
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The optimization of systems which are described by ordinary differential equations (ODEs) is often complicated by the presence of nonconvexities. A deterministic spatial branch and bound global optimization algorithm is presented in this paper for systems with ODEs in the constraints. Upper bounds for the global optimum are produced using the sequential approach for the solution of the dynamic optimization problem. The required convex relaxation of the algebraic functions is carried out using well-known global optimization techniques. A convex relaxation of the time dependent information is obtained using the concept of differential inequalities in order to construct bounds on the space of solutions of parameter dependent ODEs as well as on their second-order sensitivities. This information is then incorporated in the convex lower bounding NLP problem. The global optimization algorithm is illustrated by applying it to four case studies. These include parameter estimation problems and simple optimal control problems. The application of different underestimation schemes and branching strategies is discussed.