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Generalized Bounds for Convex Multistage Stochastic Programs

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This work was completed during my tenure as a scientific assistant and d- toral student at the Institute for Operations Research a... Weiterlesen
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Beschreibung

This work was completed during my tenure as a scientific assistant and d- toral student at the Institute for Operations Research at the University of St. Gallen. During that time, I was involved in several industry projects in the field of power management, on the occasion of which I was repeatedly c- fronted with complex decision problems under uncertainty. Although usually hard to solve, I quickly learned to appreciate the benefit of stochastic progr- ming models and developed a strong interest in their theoretical properties. Motivated both by practical questions and theoretical concerns, I became p- ticularly interested in the art of finding tight bounds on the optimal value of a given model. The present work attempts to make a contribution to this important branch of stochastic optimization theory. In particular, it aims at extending some classical bounding methods to broader problem classes of practical relevance. This book was accepted as a doctoral thesis by the University of St. Gallen in June 2004.1 am particularly indebted to Prof. Dr. Karl Frauendorfer for - pervising my work. I am grateful for his kind support in many respects and the generous freedom I received to pursue my own ideas in research. My gratitude also goes to Prof. Dr. Georg Pflug, who agreed to co-chair the dissertation committee. With pleasure I express my appreciation for his encouragement and continuing interest in my work.

Klappentext

This book investigates convex multistage stochastic programs whose objective and constraint functions exhibit a generalized nonconvex dependence on the random parameters. Although the classical Jensen and Edmundson-Madansky type bounds or their extensions are generally not available for such problems, tight bounds can systematically be constructed under mild regularity conditions. A distinct primal-dual symmetry property is revealed when the proposed bounding method is applied to linear stochastic programs. Exemplary applications are studied to assess the performance of the theoretical concepts in situations of practical relevance. It is shown how market power, lognormal stochastic processes, and risk-aversion can be properly handled in a stochastic programming framework. Numerical experiments show that the relative gap between the bounds can typically be reduced to a few percent at reasonable problem dimensions. TOC:Introduction.- Basic Theory.- Convex Stochastic Programs.- Barycentric Approximation Scheme.- Extensions.- Applications in the Power Industry.- Conclusions.



Inhalt
Basic Theory of Stochastic Optimization.- Convex Stochastic Programs.- Barycentric Approximation Scheme.- Extensions.- Applications in the Power Industry.- Conclusions.

Produktinformationen

Titel: Generalized Bounds for Convex Multistage Stochastic Programs
Autor:
EAN: 9783540269014
ISBN: 978-3-540-26901-4
Digitaler Kopierschutz: Wasserzeichen
Format: E-Book (pdf)
Herausgeber: Springer
Genre: Wirtschaft
Anzahl Seiten: 190
Veröffentlichung: 30.03.2006
Jahr: 2006
Untertitel: Englisch
Dateigrösse: 8.7 MB
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