Finitely Additive Measures and Relaxations of Extremal Problems
Published on 30. September 1996
Book
Hardback
XII, 244 pages
978-0-306-11038-2 (ISBN)
Description
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.
More details
Series
Edition
1996 ed.
Language
English
Place of publication
New York
United States
Publishing group
Springer Science+Business Media
Target group
Professional and scholarly
Research
Illustrations
XII, 244 p.
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 19 mm
Weight
559 gr
ISBN-13
978-0-306-11038-2 (9780306110382)
Schweitzer Classification
Content
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.