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Minimization with constraints described by DAEs

  • René Lamour
  • Roswitha März
  • Caren Tischendorf
Part of the Differential-Algebraic Equations Forum book series (DAEF)

Abstract

The present chapter collects results obtained by means of the projector based approach to DAEs, which are relevant in view of optimization. We do not at all undertake to offer an overview concerning the large field of control and optimization with DAE constraints and do not touch the huge arsenal of direct minimization methods. We address the basic topics of adjoint and self-adjoint DAEs and discuss the Hamiltonian property. We provide a necessary extremal conditions for the case of a nonlinear cost and a nonlinear DAE constraint. Necessary and sufficient extremal conditions are given for linear-quadratic problems. Moreover, an appropriate generalization of the Riccati feedback solution is developed. In each part, we direct particular attention to the properties of the resulting optimality DAE. If one intends to apply indirect optimization, then one should take great care to ensure good properties, such as regularity with index 1, in advance by utilizing the scope of modeling. By providing criteria in terms of the original problem data we intend to assist specialists in modeling.

Keywords

Boundary Value Problem Matrix Function Full Rank Full Column Rank Tractability Index 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • René Lamour
    • 1
  • Roswitha März
    • 1
  • Caren Tischendorf
    • 2
  1. 1.Department of MathematicsHumboldt-University of BerlinBerlinGermany
  2. 2.Mathematical InstituteUniversity of CologneCologneGermany

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