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Mathematics and Its Applications

Subdifferentials

Theory and Applications

Authors: Kusraev, A.G., Kutateladze, Semën Samsonovich

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  • ISBN 978-94-011-0265-0
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Softcover $139.99
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  • ISBN 978-94-010-4117-1
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About this book

The subject of the present book is sub differential calculus. The main source of this branch of functional analysis is the theory of extremal problems. For a start, we explicate the origin and statement of the principal problems of sub differential calculus. To this end, consider an abstract minimization problem formulated as follows: x E X, f(x) --+ inf. Here X is a vector space and f : X --+ iR is a numeric function taking possibly infinite values. In these circumstances, we are usually interested in the quantity inf f( x), the value of the problem, and in a solution or an optimum plan of the problem (i. e. , such an x that f(x) = inf f(X», if the latter exists. It is a rare occurrence to solve an arbitrary problem explicitly, i. e. to exhibit the value of the problem and one of its solutions. In this respect it becomes necessary to simplify the initial problem by reducing it to somewhat more manageable modifications formulated with the details of the structure of the objective function taken in due account. The conventional hypothesis presumed in attempts at theoretically approaching the reduction sought is as follows. Introducing an auxiliary function 1, one considers the next problem: x EX, f(x) -l(x) --+ inf. Furthermore, the new problem is assumed to be as complicated as the initial prob­ lem provided that 1 is a linear functional over X, i. e.

Table of contents (6 chapters)

  • Convex Correspondences and Operators

    Kusraev, A. G. (et al.)

    Pages 1-60

  • Geometry of Subdifferentials

    Kusraev, A. G. (et al.)

    Pages 61-136

  • Convexity and Openness

    Kusraev, A. G. (et al.)

    Pages 137-198

  • The Apparatus of Subdifferential Calculus

    Kusraev, A. G. (et al.)

    Pages 199-267

  • Convex Extremal Problems

    Kusraev, A. G. (et al.)

    Pages 268-307

Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-94-011-0265-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $139.99
price for USA in USD
  • ISBN 978-94-010-4117-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Subdifferentials
Book Subtitle
Theory and Applications
Authors
Series Title
Mathematics and Its Applications
Series Volume
323
Copyright
1995
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-94-011-0265-0
DOI
10.1007/978-94-011-0265-0
Softcover ISBN
978-94-010-4117-1
Edition Number
1
Number of Pages
IX, 405
Topics