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Asymptotic Attainability (Paperback, Softcover reprint of hardcover 1st ed. 1997)
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Asymptotic Attainability (Paperback, Softcover reprint of hardcover 1st ed. 1997)
Series: Mathematics and Its Applications, 383
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Total price: R4,324
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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.""
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