Finitely Additive Measures and Relaxations of Extremal Problems

Hardcover | September 30, 1996

byAleksander Chentsov

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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 stochastic optimization.

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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 fini...

Format:HardcoverDimensions:256 pages, 9.21 × 6.14 × 0.04 inPublished:September 30, 1996Publisher:Springer US

The following ISBNs are associated with this title:

ISBN - 10:0306110385

ISBN - 13:9780306110382

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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.