Asymptotic Attainability A.G. Chentsov

ISBN: 9789048147656

Published: December 6th 2010

Paperback

322 pages


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Asymptotic Attainability  by  A.G. Chentsov

Asymptotic Attainability by A.G. Chentsov
December 6th 2010 | Paperback | PDF, EPUB, FB2, DjVu, audiobook, mp3, RTF | 322 pages | ISBN: 9789048147656 | 8.41 Mb

In this monograph, questions of extensions and relaxations are consid ered. These questions arise in many applied problems in connection with the operation of perturbations. In some cases, the operation of small per turbations generates smallMoreIn this monograph, questions of extensions and relaxations are consid ered.

These questions arise in many applied problems in connection with the operation of perturbations. In some cases, the operation of small per turbations generates small deviations of basis indexes- a corresponding stability takes place. In other cases, small perturbations generate spas modic change of a result and of solutions defining this result. These cases correspond to unstable problems. The effect of an unstability can arise in extremal problems or in other related problems. In this connection, we note the known problem of constructing the attainability domain in con trol theory.

Of course, extremal problems and those of attainability (in abstract control theory) are connected. We exploit this connection here (see Chapter 5). However, basic attention is paid to the problem of the attainability of elements of a topological space under vanishing perturba tions of restrictions. The stability property is frequently missing- the world of unstable problems is of interest for us.

We construct regularizing proce dures. However, in many cases, it is possible to establish a certain property similar to partial stability. We call this property asymptotic nonsensitivity or roughness under the perturbation of some restrictions. The given prop erty means the following: in the corresponding problem, it is the same if constraints are weakened in some directions or not. On this basis, it is possible to construct a certain classification of constraints, selecting di rections of roughness and precision directions.



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