Optimization with PDE Constraints
10.2008β―Π³. Β· Mathematical Modelling: Theory and Applications ΠΠ½ΠΈΠ³Π° 23 Β· Springer Science & Business Media
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reportΠΡΠ΅Π½ΠΊΠΈΡΠ΅ ΠΈ ΠΎΡΠ·ΠΈΠ²ΠΈΡΠ΅ Π½Π΅ ΡΠ° ΠΏΠΎΡΠ²ΡΡΠ΄Π΅Π½ΠΈ Β ΠΠ°ΡΡΠ΅ΡΠ΅ ΠΏΠΎΠ²Π΅ΡΠ΅
ΠΡΠΈΡΠΊΠΎ Π·Π° ΡΠ°Π·ΠΈ Π΅Π»Π΅ΠΊΡΡΠΎΠ½Π½Π° ΠΊΠ½ΠΈΠ³Π°
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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ΠΡΠ΅Π½Π΅ΡΠ΅ ΡΠ°Π·ΠΈ Π΅Π»Π΅ΠΊΡΡΠΎΠ½Π½Π° ΠΊΠ½ΠΈΠ³Π°
ΠΠ°ΠΆΠ΅ΡΠ΅ Π½ΠΈ ΠΊΠ°ΠΊΠ²ΠΎ ΠΌΠΈΡΠ»ΠΈΡΠ΅.
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Π‘ΠΌΠ°ΡΡΡΠΎΠ½ΠΈ ΠΈ ΡΠ°Π±Π»Π΅ΡΠΈ
ΠΠ½ΡΡΠ°Π»ΠΈΡΠ°ΠΉΡΠ΅ ΠΏΡΠΈΠ»ΠΎΠΆΠ΅Π½ΠΈΠ΅ΡΠΎ Google Play ΠΠ½ΠΈΠ³ΠΈ Π·Π° Android ΠΈ iPad/iPhone. Π’ΠΎ Π°Π²ΡΠΎΠΌΠ°ΡΠΈΡΠ½ΠΎ ΡΠ΅ ΡΠΈΠ½Ρ
ΡΠΎΠ½ΠΈΠ·ΠΈΡΠ° Ρ ΠΏΡΠΎΡΠΈΠ»Π° Π²ΠΈ ΠΈ Π²ΠΈ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΠ²Π° Π΄Π° ΡΠ΅ΡΠ΅ΡΠ΅ ΠΎΠ½Π»Π°ΠΉΠ½ ΠΈΠ»ΠΈ ΠΎΡΠ»Π°ΠΉΠ½, ΠΊΡΠ΄Π΅ΡΠΎ ΠΈ Π΄Π° ΡΡΠ΅.
ΠΠ°ΠΏΡΠΎΠΏΠΈ ΠΈ ΠΊΠΎΠΌΠΏΡΡΡΠΈ
ΠΠΎΠΆΠ΅ΡΠ΅ Π΄Π° ΡΠ»ΡΡΠ°ΡΠ΅ Π·Π°ΠΊΡΠΏΠ΅Π½ΠΈΡΠ΅ ΠΎΡ Google Play Π°ΡΠ΄ΠΈΠΎΠΊΠ½ΠΈΠ³ΠΈ ΠΏΠΎΡΡΠ΅Π΄ΡΡΠ²ΠΎΠΌ ΡΠ΅Π± Π±ΡΠ°ΡΠ·ΡΡΠ° Π½Π° ΠΊΠΎΠΌΠΏΡΡΡΡΠ° ΡΠΈ.
ΠΠ»Π΅ΠΊΡΡΠΎΠ½Π½ΠΈ ΡΠ΅ΡΡΠΈ ΠΈ Π΄ΡΡΠ³ΠΈ ΡΡΡΡΠΎΠΉΡΡΠ²Π°
ΠΠ° Π΄Π° ΡΠ΅ΡΠ΅ΡΠ΅ Π½Π° ΡΡΡΡΠΎΠΉΡΡΠ²Π° Ρ Π΅Π»Π΅ΠΊΡΡΠΎΠ½Π½ΠΎ ΠΌΠ°ΡΡΠΈΠ»ΠΎ, ΠΊΠ°ΡΠΎ Π½Π°ΠΏΡΠΈΠΌΠ΅Ρ Π΅Π»Π΅ΠΊΡΡΠΎΠ½Π½ΠΈΡΠ΅ ΡΠ΅ΡΡΠΈ ΠΎΡ Kobo, ΡΡΡΠ±Π²Π° Π΄Π° ΠΈΠ·ΡΠ΅Π³Π»ΠΈΡΠ΅ ΡΠ°ΠΉΠ» ΠΈ Π΄Π° Π³ΠΎ ΠΏΡΠ΅Ρ
Π²ΡΡΠ»ΠΈΡΠ΅ Π½Π° ΡΡΡΡΠΎΠΉΡΡΠ²ΠΎΡΠΎ ΡΠΈ. ΠΠ·ΠΏΡΠ»Π½Π΅ΡΠ΅ ΠΏΠΎΠ΄ΡΠΎΠ±Π½ΠΈΡΠ΅ ΠΈΠ½ΡΡΡΡΠΊΡΠΈΠΈ Π² ΠΠΎΠΌΠΎΡΠ½ΠΈΡ ΡΠ΅Π½ΡΡΡ, Π·Π° Π΄Π° ΠΏΡΠ΅Ρ
Π²ΡΡΠ»ΠΈΡΠ΅ ΡΠ°ΠΉΠ»ΠΎΠ²Π΅ΡΠ΅ Π² ΠΏΠΎΠ΄Π΄ΡΡΠΆΠ°Π½ΠΈΡΠ΅ Π΅Π»Π΅ΠΊΡΡΠΎΠ½Π½ΠΈ ΡΠ΅ΡΡΠΈ.
