Computational Optimization and Applications

, Volume 36, Issue 1, pp 109–133 | Cite as

Adjoint concepts for the optimal control of Burgers equation



Adjoint techniques are a common tool in the numerical treatment of optimal control problems. They are used for efficient evaluations of the gradient of the objective in gradient-based optimization algorithms. Different adjoint techniques for the optimal control of Burgers equation with Neumann boundary control are studied. The methods differ in the point in the numerical algorithm at which the adjoints are incorporated. Discretization methods for the continuous adjoint are discussed and compared with methods applying the application of the discrete adjoint. At the example of the implicit Euler method and the Crank Nicolson method it is shown that a discretization for the adjoint problem that is adjoint to the discretized optimal control problem avoids additional errors in gradient-based optimization algorithms. The approach of discrete adjoints coincides with that of automatic differentiation tools (AD) which provide exact gradient calculations on the discrete level.


Burgers equation Optimal control Automatic differentiation Adjoint technique Discrete adjoint Newton’s method 


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© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  1. 1.Institute of Scientific ComputingTechnische Universität DresdenDresdenGermany

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