Titlebook: Optimal Control Problems for Partial Differential Equations on Reticulated Domains; Approximation and As Peter I. Kogut,Günter R. Leugering

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Springer Science+Business Media, LLC 2011

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Suboptimal and Approximate Solutions to Extremal ProblemsIn this chapter, we continue the discussion of the optimal control problems (OCPs) described in Chap. 3. Our main focus here is a proper regularization and approximation of these problems. In order to clarify the significance of these notions, we begin with the following abstract extremal problem.

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Asymptotic Analysis of Optimal Control Problems on Periodic Singular GraphsPartial differential equations (PDEs) on graphs have frequently been considered in the literature, beginning with the works of Lumer (.) and A. Vol’pert (.). We also mention Lagnese, Leugering, and Schmidt (.), Lagnese and Leugering (.), Pokornyi et al. (.), and von Below (.).

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Book 2011ing. During the development of this area, the complexity of the systems to be controlled has also increased significantly; however, the numerical realization of these complex systems has become an issue in scientific computing, as the number of variables involved may easily exceed a couple of millio

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