Stability, Approximation, and Decomposition in Two- and Multistage Stochastic Programming / Stochastic Programming (PDF)
(Sprache: Englisch)
Stochastic programming provides a framework for modelling, analyzing, and solving optimization problems with some parameters being not known up to a probability distribution. Such problems arise in a variety of applications, such as inventory control,...
Leider schon ausverkauft
eBook (pdf)
53.49 €
- Lastschrift, Kreditkarte, Paypal, Rechnung
- Kostenloser tolino webreader
Produktdetails
Produktinformationen zu „Stability, Approximation, and Decomposition in Two- and Multistage Stochastic Programming / Stochastic Programming (PDF)“
Stochastic programming provides a framework for modelling, analyzing, and solving optimization problems with some parameters being not known up to a probability distribution. Such problems arise in a variety of applications, such as inventory control, financial planning and portfolio optimization, airline revenue management, scheduling and operation of power systems, and supply chain management.
Christian Küchler studies various aspects of the stability of stochastic optimization problems as well as approximation and decomposition methods in stochastic programming. In particular, the author presents an extension of the Nested Benders decomposition algorithm related to the concept of recombining scenario trees. The approach combines the concept of cut sharing with a specific aggregation procedure and prevents an exponentially growing number of subproblem evaluations. Convergence results and numerical properties are discussed.
Christian Küchler studies various aspects of the stability of stochastic optimization problems as well as approximation and decomposition methods in stochastic programming. In particular, the author presents an extension of the Nested Benders decomposition algorithm related to the concept of recombining scenario trees. The approach combines the concept of cut sharing with a specific aggregation procedure and prevents an exponentially growing number of subproblem evaluations. Convergence results and numerical properties are discussed.
Lese-Probe zu „Stability, Approximation, and Decomposition in Two- and Multistage Stochastic Programming / Stochastic Programming (PDF)“
Chapter 3 Recombining Trees for Multistage Stochastic Programs (p. 32-33)In order to solve multistage stochastic optimization problems by numerical methods, the underlying stochastic process is usually approximated by a process that takes only a ?nite number of values. Consequently, the approximating process can be represented by a scenario tree, where the nodes of the tree correspond to the possible realizations of the process and the tree structure is induced by the ?ltration generated by the process. Unfortunately, the number of nodes can grow exponentially as the number of time stages increases, and the corresponding optimization problem thus becomes quickly intractable. Hence, many problems of practical interest are represented by stochastic programming models that include only either a small number of time stages or a small number of scenarios.
Thereby, models with a small number of time stages either take only a short time horizon into account or they allow only for a very limited branching scheme of the scenario tree. Thus, such models may appear too simpli?ed to represent dynamic decision problems. In order to construct scenario trees that approximate the initial underlying stochastic process as best as possible by a small number of scenarios, certain approximation and scenario reduction techniques have been developed by P?ug (2001), Gröwe-Kuska et al. (2003), Heitsch and Römisch (2003), and Dupacová et al. (2003). Considering only few scenarios allows to solve problems with several thousands of time stages, see, e.g., the recent case study of Eichhorn et al. (2008). However, this reduction requires some compromise with regard to the representation of the underlying stochastic process.
An approach often used in practice, aiming to ?nd acceptable decisions along a concrete observation process, is to optimize with a rolling time horizon (cf., e.g., Sethi and Sorger (1991)). Thereby, a solution is constructed by solving a sequence
... mehr
of subproblems on small overlapping time intervals. However, decisions made by considering only a short time horizon will be myopic and thus generally not optimal whenever the optimization problem includes time-coupling constraints. The situation can be somewhat improved by ?nding suitable (shadow-) prices for those decision variables that a?ect the future costs.
A further approach to handle problems of larger dimensionality relies on recombining scenario trees. The probably best-known example is the Binomial Model of Stock Price Behaviour due to Cox, Ross, and Rubinstein (1979), where the node number of a binary scenario tree with T time stages decreases from 2T -1 to T(T +1)/2 by the recombination of scenarios. However, in a recombined node no information about the history of the parameter and the decision processes is available. Consequently, recombining scenario trees seem at ?rst sight not appropriate to solve optimization problems including time-coupling constraints.
A further approach to handle problems of larger dimensionality relies on recombining scenario trees. The probably best-known example is the Binomial Model of Stock Price Behaviour due to Cox, Ross, and Rubinstein (1979), where the node number of a binary scenario tree with T time stages decreases from 2T -1 to T(T +1)/2 by the recombination of scenarios. However, in a recombined node no information about the history of the parameter and the decision processes is available. Consequently, recombining scenario trees seem at ?rst sight not appropriate to solve optimization problems including time-coupling constraints.
... weniger
Autoren-Porträt von Christian Küchler
Dr. Christian Küchler completed his doctoral thesis at the Humboldt University, Berlin. He currently works as a quantitative analyst at Landesbank Berlin AG.
Bibliographische Angaben
- Autor: Christian Küchler
- 2010, 2009, 184 Seiten, Englisch
- Verlag: Vieweg+Teubner Verlag
- ISBN-10: 3834893994
- ISBN-13: 9783834893994
- Erscheinungsdatum: 30.05.2010
Abhängig von Bildschirmgröße und eingestellter Schriftgröße kann die Seitenzahl auf Ihrem Lesegerät variieren.
eBook Informationen
- Dateiformat: PDF
- Größe: 2.56 MB
- Ohne Kopierschutz
- Vorlesefunktion
Sprache:
Englisch
Kommentar zu "Stability, Approximation, and Decomposition in Two- and Multistage Stochastic Programming / Stochastic Programming"
0 Gebrauchte Artikel zu „Stability, Approximation, and Decomposition in Two- and Multistage Stochastic Programming / Stochastic Programming“
Zustand | Preis | Porto | Zahlung | Verkäufer | Rating |
---|
Schreiben Sie einen Kommentar zu "Stability, Approximation, and Decomposition in Two- and Multistage Stochastic Programming / Stochastic Programming".
Kommentar verfassen