Abstract
A class of optimal control problems for a parabolic equation with nonlinear boundary condition and constraints on the control and the state is considered. Associated approximate problems are established, where the equation of state is defined by a semidiscrete Ritz-Galerkin method. Moreover, we are able to allow for the discretization of admissible controls. We show the convergence of the approximate controls to the solution of the exact control problem, as the discretization parameter tends toward zero. This result holds true under the assumption of a certain sufficient second-order optimality condition.
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Communicated by I. Lasiecka
Dedicated to the 60th birthday of Lothar von Wolfersdorf
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Tröltzsch, F. Semidiscrete Ritz-Galerkin approximation of nonlinear parabolic boundary control problems—Strong convergence of optimal controls. Appl Math Optim 29, 309–329 (1994). https://doi.org/10.1007/BF01189480
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DOI: https://doi.org/10.1007/BF01189480
Key words
- Optimal control
- Parabolic equation
- Nonlinear boundary condition
- State constraint
- Ritz-Galerkin approximation