Summary
A boundary optimal control problem for an instationary nonlinear reaction-diffusion equation system in three spatial dimensions is presented. The control is subject to pointwise control constraints and a penalized integral constraint. Under a coercivity condition on the Hessian of the Lagrange function, an optimal solution is shown to be a directionally differentiable function of perturbation parameters such as the reaction and diffusion constants or desired and initial states. The solution’s derivative, termed parametric sensitivity, is characterized as the solution of an auxiliary linear-quadratic optimal control problem. A numerical example illustrates the utility of parametric sensitivities which allow a quantitative and qualitative perturbation analysis of optimal solutions.
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Griesse, R., Volkwein, S. (2006). Parametric Sensitivity Analysis for Optimal Boundary Control of a 3D Reaction-Diffusion System. In: Di Pillo, G., Roma, M. (eds) Large-Scale Nonlinear Optimization. Nonconvex Optimization and Its Applications, vol 83. Springer, Boston, MA. https://doi.org/10.1007/0-387-30065-1_9
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DOI: https://doi.org/10.1007/0-387-30065-1_9
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