Finitely Additive Measures and Relaxations of Extremal Problems / Edition 1

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This monograph constructs correct extensions of extremal problems, including problems of multicriteria optimization as well as more general cone optimization problems. The author obtains common conditions of stability and asymptotic nonsensitivity of extremal problems under perturbation of a part of integral restrictions for finite and infinite systems of restrictions. Features include individual chapters on nonstandard approximation of finitely additive measures by indefinite integrals and constructions of attraction sets. Professor Chentsov illustrates abstract settings by providing examples of problems of impulse control, mathematical programming, and shastic optimization.

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Editorial Reviews

Examines the extension of extremal problems in the class of finitely additive measures, focusing on regularizing settings for real-life applications. Contains chapters on relaxations of and compactificators in extremal problems; finitely additive measures on a semialgebra of sets; finitely additive measures and indefinite integrals; admissible sets and their relaxations; relaxations of attainable sets; asymptotic values and their generalized representation; asymptotic efficiency; and issues of computations stability. Annotation c. Book News, Inc., Portland, OR (
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Product Details

  • ISBN-13: 9780306110382
  • Publisher: Springer-Verlag New York, LLC
  • Publication date: 9/1/1996
  • Series: Monographs in Contemporary Mathematics Series
  • Edition description: 1996
  • Edition number: 1
  • Pages: 244
  • Product dimensions: 0.69 (w) x 6.14 (h) x 9.21 (d)

Table of Contents

Introduction. Relaxation of Extremal Problems (Intuitive Discussion and Examples). Compactificators in Extremal Problems. Finitely Additive Measures on Semialgebras of Sets. Finitely Additive Measures and Indefinite Integrals. Admissible Sets and Their Relaxation. Relaxations of Attainable Sets. Asymptotic Values and Their Generalized Representation. Asymptotic Effectiveness. Questions of Stability with Respect to the Result. Conclusion. Index.

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