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Optimization with PDE Constraints (Hardcover, 2009 ed.)
Loot Price: R4,271
Discovery Miles 42 710
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Optimization with PDE Constraints (Hardcover, 2009 ed.)
Series: Mathematical Modelling: Theory and Applications, 23
Expected to ship within 10 - 15 working days
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Solving optimization problems subject to constraints given in terms
of partial d- ferential equations (PDEs) with additional
constraints on the controls and/or states is one of the most
challenging problems in the context of industrial, medical and
economical applications, where the transition from model-based
numerical si- lations to model-based design and optimal control is
crucial. For the treatment of such optimization problems the
interaction of optimization techniques and num- ical simulation
plays a central role. After proper discretization, the number of
op- 3 10 timization variables varies between 10 and 10 . It is only
very recently that the enormous advances in computing power have
made it possible to attack problems of this size. However, in order
to accomplish this task it is crucial to utilize and f- ther
explore the speci?c mathematical structure of optimization problems
with PDE constraints, and to develop new mathematical approaches
concerning mathematical analysis, structure exploiting algorithms,
and discretization, with a special focus on prototype applications.
The present book provides a modern introduction to the rapidly
developing ma- ematical ?eld of optimization with PDE constraints.
The ?rst chapter introduces to the analytical background and
optimality theory for optimization problems with PDEs. Optimization
problems with PDE-constraints are posed in in?nite dim- sional
spaces. Therefore, functional analytic techniques, function space
theory, as well as existence- and uniqueness results for the
underlying PDE are essential to study the existence of optimal
solutions and to derive optimality conditions.
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