Titlebook: Hierarchical Optimization and Mathematical Physics; Vladimir Tsurkov Book 2000 Springer Science+Business Media Dordrecht 2000 Optimal cont

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Hierarchical Systems of Mathematical Physics,l problems. We introduce a special class of hierarchical optimal control problems. These are two-level systems, whose subsystems are models of mathematical physics. First, we give a statement of dynamic separable block problems with ordinary differential equations and present the main constructions

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Effectiveness of Decomposition, We consider dynamical problems of optimal control. Their solution through the use of the maximum principle results in cumbersome computations. The application of two-level decomposition or the reduction method to linear quadratic problems amounts to solving simple problems of lower dimensions.

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Appendix. The Main Approaches in Hierarchical Optimization,is fairly well covered in the literature, therefore, we present it briefly here, just to introduce the main ideas. The Kornai-Liptak decomposition principle is presented more comprehensively. Along with the main published constructions, we consider various schemes of reducing dimension based on the

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Hierarchical Systems of Mathematical Physics,ntial equations of different types. To justify the method, we use the concept of weak solutions in functional spaces. Lastly, we study the block linear quadratic optimal control problems. We describe an analytical method to decrease dimensions, based on the reducing the systems of linear algebraic e

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Appendix. The Main Approaches in Hierarchical Optimization,mization. Finally, the use of the Lagrange functional for the organization of the two-level iterative process with respect to primal and dual variables allows us to formulate a fairly universal approach to reducing dimensions in block problems of optimal control.

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Hierarchical Optimization and Mathematical Physics

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1384-6485 functions). Thus, we bridge the gap between two disciplines: optimization theory of large-scale systems and mathematical physics. The first motivation was a spe978-1-4613-7112-0978-1-4615-4667-2Series ISSN 1384-6485