Viability theory
Optimal control drug scheduling of cancer chemotherapy
Automatica (Journal of IFAC)
CVODE, a stiff/nonstiff ODE solver in C
Computers in Physics
State event location in differential-algebraic models
ACM Transactions on Modeling and Computer Simulation (TOMACS)
A Rigorous Global Optimization Algorithm for Problems with Ordinary Differential Equations
Journal of Global Optimization
Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.)
Global Optimization with Nonlinear Ordinary Differential Equations
Journal of Global Optimization
Bounding the Solutions of Parameter Dependent Nonlinear Ordinary Differential Equations
SIAM Journal on Scientific Computing
On Taylor Model Based Integration of ODEs
SIAM Journal on Numerical Analysis
McCormick-Based Relaxations of Algorithms
SIAM Journal on Optimization
Discretize-then-relax approach for convex/concave relaxations of the solutions of parametric ODEs
Applied Numerical Mathematics
Generalized McCormick relaxations
Journal of Global Optimization
Convergence rate of McCormick relaxations
Journal of Global Optimization
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A new method is described for computing nonlinear convex and concave relaxations of the solutions of parametric ordinary differential equations (ODEs). Such relaxations enable deterministic global optimization algorithms to be applied to problems with ODEs embedded, which arise in a wide variety of engineering applications. The proposed method computes relaxations as the solutions of an auxiliary system of ODEs, and a method for automatically constructing and numerically solving appropriate auxiliary ODEs is presented. This approach is similar to two existing methods, which are analyzed and shown to have undesirable properties that are avoided by the new method. Two numerical examples demonstrate that these improvements lead to significantly tighter relaxations than previous methods.