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Representation of the Lagrange Multipliers for Optimal Control Problems Subject to Differential-Algebraic Equations of Index Two

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  • M. Gerdts

    (University of Hamburg)

Abstract

Necessary conditions are derived for optimal control problems subject to index-2 differential-algebraic equations, pure state constraints, and mixed control-state constraints. Differential-algebraic equations are composite systems of differential equations and algebraic equations, which arise frequently in practical applications. The structure of the optimal control problem under consideration is exploited and special emphasis is laid on the representation of the Lagrange multipliers resulting from the necessary conditions for infinite optimization problems.

Suggested Citation

  • M. Gerdts, 2006. "Representation of the Lagrange Multipliers for Optimal Control Problems Subject to Differential-Algebraic Equations of Index Two," Journal of Optimization Theory and Applications, Springer, vol. 130(2), pages 231-251, August.
    • Handle: RePEc:spr:joptap:v:130:y:2006:i:2:d:10.1007_s10957-006-9100-1
    DOI: 10.1007/s10957-006-9100-1
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    References listed on IDEAS

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    1. M. Gerdts, 2003. "Direct Shooting Method for the Numerical Solution of Higher-Index DAE Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 117(2), pages 267-294, May.
    2. M. Gerdts, 2006. "Local Minimum Principle for Optimal Control Problems Subject to Differential-Algebraic Equations of Index Two," Journal of Optimization Theory and Applications, Springer, vol. 130(3), pages 443-462, September.
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    Cited by:

    1. Matthias Gerdts & Björn Hüpping, 2012. "Virtual control regularization of state constrained linear quadratic optimal control problems," Computational Optimization and Applications, Springer, vol. 51(2), pages 867-882, March.
    2. Matthias Gerdts & Martin Kunkel, 2011. "A globally convergent semi-smooth Newton method for control-state constrained DAE optimal control problems," Computational Optimization and Applications, Springer, vol. 48(3), pages 601-633, April.

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