Stable Parametric Programming: 57 - Rilegato

Zlobec, S.

 
9780792371397: Stable Parametric Programming: 57
Rilegato
ISBN 10: 0792371399 ISBN 13: 9780792371397
Casa editrice: SPRINGER NATURE, 2001

Sinossi

Optimality and stability are two important notions in applied mathematics. This book is a study of these notions and their relationship in linear and convex parametric programming models. It begins with a survey of basic optimality conditions in nonlinear programming. Then new results in convex programming, using LFS functions, for single-objective, multi-objective, differentiable and non-smooth programs are introduced. Parametric programming models are studied using basic tools of point-to-set topology. Stability of the models is introduced, essentially, as continuity of the feasible set of decision variables under continuous perturbations of the parameters. Perturbations that preserve this continuity are regions of stability. It is shown how these regions can be identified. The main results on stability are characterizations of locally and globally optimal parameters for stable and also for unstable perturbations. The results are straightened for linear models and bi-level programs. Some of the results are extended to abstract spaces after considering parameters as "controls". Illustrations from diverse fields, such as data envelopment analysis, management, von Stackelberg games of market economy, and navigation problems are given and several case studies are solved by finding optimal parameters. The book has been written in an analytic spirit.

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Recensione

'The book would be of great interest to both graduate students and researchers who are concerned with optimization problems.'
Zentalblatt MATH, 986 (2002)

Contenuti

General Preface. Preface. Acknowledgements. 1. Introduction. 2. Classical Optimality Conditions. 3. Basic Convex Programming. 4. Asymptotic Optimality Conditions. 5. Non-Smooth Programs. 6. Multi-Objective Programs. 7. Introduction to Stability. 8. Locally Optimal Parameters. 9. Globally Optimal Parameters. 10. Optimal Value Function. 11. Partly Convex Programming. 12. Numerical Methods in PCP. 13. Zermelo's Navigation Problems. 14. Efficiency Testing in Data Envelopment Analysis. 15. Orientation. Appendix: Method of Weierstrass. Glossary of Symbols. References. Index.

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Editore
SPRINGER NATURE
Data di pubblicazione
2001
Lingua
Inglese
ISBN 10 
0792371399
ISBN 13 
9780792371397
Rilegatura
Copertina rigida
Numero di pagine
322
Contatto del produttore
non disponibile
Persona responsabile
ProductSafety@springernature.com
ProductSafety@springernature.com

Poststr. 9
Darmstadt
64293
Germania

Altre edizioni note dello stesso titolo

9781461348856: Stable Parametric Programming: 57

Edizione in evidenza

ISBN 10:  1461348854 ISBN 13:  9781461348856
Casa editrice: Springer, 2013
Brossura