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Title

Solving optimization-constrained differential equations with discontinuity points, with applications to atmospheric chemistry

Authors
Landry, Chantal
Caboussat, Alexandre
Published in SIAM Journal on Scientific Computing. 2009, vol. 31, p. 3806-3826
Abstract Ordinary differential equations are coupled with constrained optimization problems when modeling a system at equilibrium evolving with time. Discontinuity points are created by the activation/deactivation of inequality constraints. A numerical method for the resolution of optimization-constrained differential equations is proposed by coupling an implicit Runge-Kutta method (RADAU5), with numerical techniques for the detection of the events (activation and deactivation of constraints) when the system evolves with time. The computation of the events is based on dense output formulas, continuation techniques and geometric arguments. Numerical results are presented for the simulation of the time-dependent equilibrium of organic atmospheric aerosol particles, and show the efficiency and accuracy of the approach.
Keywords Initial value problemsDifferential-algebraic equationsConstrained optimizationRunge-Kutta methodsEvent detectionDiscontinuity pointsComputational chemistry.
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LANDRY, Chantal, CABOUSSAT, Alexandre, HAIRER, Ernst. Solving optimization-constrained differential equations with discontinuity points, with applications to atmospheric chemistry. In: SIAM Journal on Scientific Computing, 2009, vol. 31, p. 3806-3826. https://archive-ouverte.unige.ch/unige:5212

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Deposited on : 2010-02-16

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