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Connectedness and Necessary Conditions for an Extremum (Mathematics and Its Applications) | 
 enlarge | Author: A.p. Abramov
Publisher: Springer
Category: Book
List Price: $135.00
Buy New: $125.02
You Save: $9.98 (7%)
New (14) Used (8) from $95.00
Sales Rank: 3884538
Media: Hardcover
Edition: 1
Pages: 212
Number Of Items: 1
Shipping Weight (lbs): 0.3
Dimensions (in): 9.6 x 6.4 x 0.8
ISBN: 0792349105
Dewey Decimal Number: 519.3
EAN: 9780792349105
Publication Date: March 31, 1998
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Condition: New American book. Printed on demand and shipped within the US in 4-7 days (expedited) or about 10-14 days (standard). Standard can occasionally be slower so we advise using expedited if quicker delivery is important!
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Product Description
This monograph is the first book in the study of necessary conditions of an extremum in which topological connectedness plays a major role. Many new and original results are presented here. The synthesis of the well-known Dybrovitskii-Milyutin approach, based on functional analysis, and topological methods permits the derivation of the so-called alternative conditions of an extremum: if the Euler equation has the trivial solution only at an extreme point, then some inclusion is valid for the functionals belonging to the dual space. Also, the present approach gives a transparent answer to the question why the Kuhn-Tucker theorem establishes the restrictions on the signs of the Lagrange multipliers for the inequality constraints but why this theorem does not establish any analogous restrictions on the multipliers for the equality constraints.
Examples from mathematical economics illustrate the alternative conditions of any extremum. Parallels are drawn between these examples and the problems of static equilibrium in classical mechanics.
Audience: This volume will be of use to mathematicians and graduate students interested in the areas of optimization, optimal control and mathematical economics.
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