Symbolic elimination in dynamic optimization based on block-triangular ordering

Fredrik Magnusson, Johan Åkesson

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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 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.
Original languageEnglish
Pages (from-to)92-119
JournalOptimization Methods and Software
Issue number1
Early online date2017 Jan 7
Publication statusPublished - 2018 Jan 2

Subject classification (UKÄ)

  • Computational Mathematics

Free keywords

  • dynamic optimization
  • differential-algebraic equations
  • block-triangular ordering
  • tearing
  • sparsity preservation
  • nonlinear programming
  • Modelica


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