Asymptotic Attainability

A.G. Chentsov (Autor)

Buch | Softcover

322 Seiten

2010 | Softcover reprint of hardcover 1st ed. 1997
Springer (Verlag)
978-90-481-4765-6 (ISBN)

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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 "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".

1 Asymptotically Attainable Elements: Model Examples.- 2 Asymptotic Effects in Linear Control Problems with Integral Constraints.- 3 Asymptotic Attainability: General Questions.- 4 Asymptotic Attainability under Perturbation of Integral Constraints.- 5 Relaxations of Extremal Problems.- 6 Some Generalizations.- 7 Other Extension Constructions in the Space of Solutions.- Conclusion.- List of notations.

Erscheint lt. Verlag	6.12.2010
Reihe/Serie	Mathematics and Its Applications ; 383
Zusatzinfo	XIV, 322 p.
Verlagsort	Dordrecht
Sprache	englisch
Maße	210 x 279 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	90-481-4765-4 / 9048147654
ISBN-13	978-90-481-4765-6 / 9789048147656
Zustand	Neuware