Numerische Mathematik

, Volume 87, Issue 2, pp 247–282 | Cite as

Runge-Kutta methods in optimal control and the transformed adjoint system

  • William W. Hager


The convergence rate is determined for Runge-Kutta discretizations of nonlinear control problems. The analysis utilizes a connection between the Kuhn-Tucker multipliers for the discrete problem and the adjoint variables associated with the continuous minimum principle. This connection can also be exploited in numerical solution techniques that require the gradient of the discrete cost function.

Mathematics Subject Classification (1991): 49M25, 65L06 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • William W. Hager
    • 1
  1. 1.Department of Mathematics, University of Florida, Gainesville, FL 32611, USA; e-mail:,

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