Adaptive multiple shooting for boundary value problems and constrained parabolic optimization problems. (English) Zbl 1326.49001
Heidelberg: Univ. Heidelberg, Naturwissenschaftlich-Mathematische Gesamtfakultät (Diss.). iv, 190 p. (2015).
The thesis is written on the development of adaptive techniques for multiple shooting methods. The goal of the present work lies in the use of optimal control problems in the spirit of parabolic PDEs. The study is carried out under suitable constraints on the control variable in the multiple shooting context. The emphasis is put on an algorithmic approach which allows an extended comparison of the different shooting schemes. It is a nice work, written in an active domain of research.
Reviewer: John T. Coletsos (Athens)
MSC:
49-02 | Research exposition (monographs, survey articles) pertaining to calculus of variations and optimal control |
49M25 | Discrete approximations in optimal control |
49M15 | Newton-type methods |
49M27 | Decomposition methods |
49J20 | Existence theories for optimal control problems involving partial differential equations |
35K99 | Parabolic equations and parabolic systems |
93C40 | Adaptive control/observation systems |
65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
65M55 | Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs |