Abstract
In this paper, we study the approximation by the penalty method of a control problem governed by a pseudo-parabolic equation with a noncoercive control functional and with control and state constraints. The existence of solutions to the penalized problems is established. In addition, the convergence of the penalized problems to the solution, the Lagrange multipliers, and the minimum value of the original problem is studied. The results apply to Sobolev and parabolic equations as well.
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Communicated by L. D. Berkovitz
This work was partially supported by the National Science Foundation, Grant No. MCS-79-02037. The author would like to thank Professor A. B. Schwarzkopf for his helpful comments on this paper.
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White, L.W. Penalty approximation of a Sobolev optimal control problem with state constraints. J Optim Theory Appl 33, 121–135 (1981). https://doi.org/10.1007/BF00935181
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DOI: https://doi.org/10.1007/BF00935181