2017
DOI: 10.1080/10556788.2016.1270944
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Symbolic elimination in dynamic optimization based on block-triangular ordering

Abstract: We consider dynamic optimization problems for systems described by differential-algebraic equations (DAEs). Such problems are usually solved by discretizing the full DAE. We propose techniques to symbolically eliminate many of the algebraic variables in a preprocessing step before discretization. These techniques are inspired by the causalization and tearing techniques often used when solving DAE initial value problems. Since sparsity is crucial for some dynamic optimization methods, we also propose a novel ap… Show more

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Cited by 6 publications
(3 citation statements)
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“…As demonstrated in (Magnusson and Åkesson, 2016), and as we will also see is the case in this work, the symbolic elimination not only reduces the solution time, but also improves convergence robustness, that is, probability of successfully solving an optimization problem in a timely manner.…”
Section: Symbolic Eliminationmentioning
confidence: 80%
See 1 more Smart Citation
“…As demonstrated in (Magnusson and Åkesson, 2016), and as we will also see is the case in this work, the symbolic elimination not only reduces the solution time, but also improves convergence robustness, that is, probability of successfully solving an optimization problem in a timely manner.…”
Section: Symbolic Eliminationmentioning
confidence: 80%
“…There has been recent work carried out (Magnusson and Åkesson, 2016) to address this problem in general by applying a block-lower triangular (BLT) transformation of the DAE to identify algebraic variables that only depend affinely on the corresponding block variables. This allows symbolic elimination of such variables by forward substitution.…”
Section: Symbolic Eliminationmentioning
confidence: 99%
“…These enhancements share that the computation of y for a given z only involves fast and numerically stable algorithms such as solving implicit univariate equations or small systems of equations. Another recent approach tries to balance between minimizing the border width and preserving the sparsity during the elimination (Magnusson and Åkesson, 2017). The reader is referred to (Baharev et al, 2017a) for an in-depth discussion of the variations on tearing.…”
Section: Introductionmentioning
confidence: 99%