Numerical simulation of differential-algebraic equations with embedded global optimization criteria

Optimization methods & software, vol. 41, pp. 509–523

Abstract

We are considering differential-algebraic equations with embedded optimization criteria (DAEOs), in which the embedded optimization problem is solved by global optimization. This leads to differential inclusions for cases in which there are multiple global optimizers at the same time. Jump events from one global optimum to another result in nonsmooth DAEs and reduce the order of convergence of the numerical integrator to first-order. Implementation of event detection and location as introduced in this work preserves the higher-order convergence behaviour of the integrator. This allows the computation of discrete tangent and adjoint sensitivities for optimal control problems.

Authors 3

1. Jens Deussen corresponding Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University

   Informatik 12: Software and Tools for Computational Engineering, RWTH Aachen University, Aachen, Germany

2. Jonathan Hüser Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University

   Informatik 12: Software and Tools for Computational Engineering, RWTH Aachen University, Aachen, Germany

3. Uwe Naumann Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University

   Informatik 12: Software and Tools for Computational Engineering, RWTH Aachen University, Aachen, Germany