Optimal control in first-order Sobolev spaces with inequality constraints View Full Text


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Article Info

DATE

2019-04

AUTHORS

Yu Deng, Patrick Mehlitz, Uwe Prüfert

ABSTRACT

In this paper, an elliptic optimal control problem with controls from H1(Ω) which have to satisfy standard box constraints is considered. Thus, Lagrange multipliers associated with the box constraints are, in general, elements of H1(Ω)⋆ as long as the lower and upper bound belong to H1(Ω) as well. If these bounds possess less regularity, the overall existence of a Lagrange multiplier is not even guaranteed. In order to avoid the direct solution of a not necessarily available KKT system, a penalty method is suggested which finds the minimizer of the control-constrained problem. Its convergence properties are analyzed. Furthermore, some numerical strategies for the computation of optimal solutions are suggested and illustrated. More... »

PAGES

1-30

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10589-018-0053-8

DOI

http://dx.doi.org/10.1007/s10589-018-0053-8

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1111033060


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