Abstract
Elliptic control problems with a quadratic cost functional require the solution of a system of two elliptic boundary-value problems. We propose a fast iterative process for the numerical solution of this problem. The method can be applied to very special problems (for example, Poisson equation for a rectangle) as well as to general equations (arbitrary dimensions, general region). Also, nonlinear problems can be treated. The work required is proportional to the work taken by the numerical solution of a single elliptic equation.
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Communicated by L. Cesari
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Hackbusch, W. Fast solution of elliptic control problems. J Optim Theory Appl 31, 565–581 (1980). https://doi.org/10.1007/BF00934478
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DOI: https://doi.org/10.1007/BF00934478