Improved relaxations for the parametric solutions of ODEs using differential inequalities
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Publication:367169
DOI10.1007/s10898-012-9909-0zbMath1273.49034OpenAlexW2079800122MaRDI QIDQ367169
Paul I. Barton, Joseph K. Scott
Publication date: 26 September 2013
Published in: Journal of Global Optimization (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10898-012-9909-0
Numerical methods based on nonlinear programming (49M37) Numerical methods for initial value problems involving ordinary differential equations (65L05) Differential inequalities involving functions of a single real variable (34A40) Numerical methods of relaxation type (49M20)
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Cites Work
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- Discretize-then-relax approach for convex/concave relaxations of the solutions of parametric ODEs
- Convergence rate of McCormick relaxations
- Generalized McCormick relaxations
- Global solution of optimization problems with parameter-embedded linear dynamic systems.
- A rigorous global optimization algorithm for problems with ordinary differential equations
- Bounds on the reachable sets of nonlinear control systems
- Cancer immunotherapy, mathematical modeling and optimal control
- Global optimization with nonlinear ordinary differential equations
- Nonlinear convex and concave relaxations for the solutions of parametric ODEs
- A Comparison of the Optimal Costs of Two Canonical Inventory Systems
- McCormick-Based Relaxations of Algorithms
- Computability of global solutions to factorable nonconvex programs: Part I — Convex underestimating problems
- State event location in differential-algebraic models
- On Taylor Model Based Integration of ODEs
- Bounding the Solutions of Parameter Dependent Nonlinear Ordinary Differential Equations
- Viability theory
