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Типовість розв'язності деяких задач оптимального керування
Let E be a real Banach space, X a nonempty weak compact subset of E, B a closed convex subset of E such that 0 belongs int B, and f : X → R be a bounded from above weak upper semicontinuous functional. It is proved that the set of all y belongs E, for which the problem f(x)+μβ(x − y) → sup x belongs...
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| Main Author: | |
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| Format: | Article |
| Language: | Ukrainian |
| Published: |
Видавничий дім "Академперіодика" НАН України
2008
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| Subjects: | |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/5754 |
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| Summary: | Let E be a real Banach space, X a nonempty weak compact subset of E, B a closed convex subset of E such that 0 belongs int B, and f : X → R be a bounded from above weak upper semicontinuous functional. It is proved that the set of all y belongs E, for which the problem f(x)+μβ(x − y) → sup x belongs X, where μβ is the Minkowski functional of B, has a solution, contains an Gδ-set dense in E. This result is used for proving the generic solvability optimal control problems for linear systems. |
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