Convex and concave relaxations for the parametric solutions of semi-explicit index-one differential-algebraic equations

DOI10.1007/s10957-012-0149-8zbMath1284.65095OpenAlexW2087741918MaRDI QIDQ1949566

Joseph K. Scott, Paul I. Barton

Publication date: 8 May 2013

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10957-012-0149-8

zbMATH Keywords

global optimizationoptimal controldynamic optimizationconvex relaxationparametric solutionsconcave overestimatorconvex underestimatorindex-one differential algebraic equations

Mathematics Subject Classification ID

Implicit ordinary differential equations, differential-algebraic equations (34A09) Numerical methods for differential-algebraic equations (65L80) Control/observation systems governed by ordinary differential equations (93C15) Nonlinear ordinary differential operators (34L30) Numerical methods of relaxation type (49M20)

Related Items (8)

Extended McCormick relaxation rules for handling empty arguments representing infeasibility ⋮ Nonsmooth DAEs with Applications in Modeling Phase Changes ⋮ Convergence-order analysis for differential-inequalities-based bounds and relaxations of the solutions of ODEs ⋮ Differentiable McCormick relaxations ⋮ Reachability Analysis and Deterministic Global Optimization of DAE Models ⋮ Global Optimization of Mixed-Integer ODE Constrained Network Problems Using the Example of Stationary Gas Transport ⋮ Optimal fixed-levels control for nonlinear systems with quadratic cost-functionals ⋮ Global dynamic optimization with Hammerstein-Wiener models embedded

Uses Software

• SUNDIALS
• CVODE
• libMC

Cites Work

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• SUNDIALS
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• Interval Methods for Systems of Equations
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• Finite-Dimensional Variational Inequalities and Complementarity Problems
• On Taylor Model Based Integration of ODEs
• Bounding the Solutions of Parameter Dependent Nonlinear Ordinary Differential Equations
• Ordinary Differential Equations

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