Finitely Additive Measures and Relaxations of Extremal Problems / Edition 1

Finitely Additive Measures and Relaxations of Extremal Problems / Edition 1

by A.G. Chentsov
     
 

ISBN-10: 0306110385

ISBN-13: 9780306110382

Pub. Date: 09/01/1996

Publisher: Springer-Verlag New York, LLC

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

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Overview

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.

Product Details

ISBN-13:
9780306110382
Publisher:
Springer-Verlag New York, LLC
Publication date:
09/01/1996
Series:
Monographs in Contemporary Mathematics Series
Edition description:
1996
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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