A Second Order Scheme for Solving Optimization-Constrained Differential Equations with Discontinuities

A. Caboussat () and C. Landry ()
Additional contact information
A. Caboussat: University of Houston, Department of Mathematics
C. Landry: Ecole Polytechnique Fédérale de Lausanne, Institute of Analysis and Scientific Computing

A chapter in Numerical Mathematics and Advanced Applications, 2008, pp 761-768 from Springer

Abstract: Abstract A numerical method for the resolution of a system of ordinary differential equations coupled with a mixed constrained minimization problem is presented. This coupling induces discontinuities of some time-dependent variables when inequality constraints are activated or deactivated. The ordinary differential equations are discretized in time and combined with the first order optimality conditions of the optimization problem. We use a second order multistep method based on a predictor-corrector Adams scheme to detect the discontinuities by extrapolation of the trajectories. Optimization features, namely a sensitivity analysis, are exploited to compute the derivatives of the optimization variables and track the discontinuity points. The main difficulty consists in the impossibility of defining an explicit event function to characterize the activation or deactivation of a constraint. The order of convergence of our method is proved when inequality constraints are activated and numerical results for atmospheric organic particles are presented.

Keywords: Inequality Constraint; Discontinuity Point; Dynamic Optimization Problem; Order Optimality Condition; Exact Trajectory (search for similar items in EconPapers)
Date: 2008
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-69777-0_91

Ordering information: This item can be ordered from
http://www.springer.com/9783540697770

DOI: 10.1007/978-3-540-69777-0_91

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().