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Symbolic elimination in dynamic optimization based on block-triangular ordering

Magnusson, Fredrik LU and Åkesson, Johan (2018) In Optimization Methods and Software 33(1). p.92-119
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 approach to preserving sparsity during this procedure.

The proposed methods have been implemented in the open-source JModelica.org platform. We evaluate the performance of the methods on a suite of optimal control problems... (More)
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 approach to preserving sparsity during this procedure.

The proposed methods have been implemented in the open-source JModelica.org platform. We evaluate the performance of the methods on a suite of optimal control problems solved using direct collocation.
We consider both computational time and probability of solving the problem in a timely manner. We demonstrate that the proposed methods often are an order of magnitude faster than the standard way of discretizing the full DAE, and also significantly increase probability of successful convergence. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
dynamic optimization, differential-algebraic equations, block-triangular ordering, tearing, sparsity preservation, nonlinear programming, Modelica
in
Optimization Methods and Software
volume
33
issue
1
pages
92 - 119
publisher
Taylor & Francis
external identifiers
  • scopus:85009782173
ISSN
1055-6788
DOI
10.1080/10556788.2016.1270944
language
English
LU publication?
yes
id
c6fd37fe-6325-43c8-9dbd-e13a255b4771
date added to LUP
2016-12-30 13:24:48
date last changed
2018-02-18 23:56:05
@article{c6fd37fe-6325-43c8-9dbd-e13a255b4771,
  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 approach to preserving sparsity during this procedure.<br/><br/>The proposed methods have been implemented in the open-source JModelica.org platform. We evaluate the performance of the methods on a suite of optimal control problems solved using direct collocation.<br/>We consider both computational time and probability of solving the problem in a timely manner. We demonstrate that the proposed methods often are an order of magnitude faster than the standard way of discretizing the full DAE, and also significantly increase probability of successful convergence.},
  author       = {Magnusson, Fredrik and Åkesson, Johan},
  issn         = {1055-6788},
  keyword      = {dynamic optimization,differential-algebraic equations,block-triangular ordering,tearing,sparsity preservation,nonlinear programming,Modelica},
  language     = {eng},
  month        = {01},
  number       = {1},
  pages        = {92--119},
  publisher    = {Taylor & Francis},
  series       = {Optimization Methods and Software},
  title        = {Symbolic elimination in dynamic optimization based on block-triangular ordering},
  url          = {http://dx.doi.org/10.1080/10556788.2016.1270944},
  volume       = {33},
  year         = {2018},
}