Descent Directions and Efficient Solutions in Discretely Distributed Stochastic Programs:
In engineering and economics a certain vector of inputs or decisions must often be chosen, subject to some constraints, such that the expected costs arising from the deviation between the output of a stochastic linear system and a desired stochastic target vector are minimal. In many cases the loss...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1988
|
| Ausgabe: | 1st ed. 1988 |
| Schriftenreihe: | Lecture Notes in Economics and Mathematical Systems
299 |
| Schlagworte: | |
| Online-Zugang: | BTU01 URL des Erstveröffentlichers |
| Zusammenfassung: | In engineering and economics a certain vector of inputs or decisions must often be chosen, subject to some constraints, such that the expected costs arising from the deviation between the output of a stochastic linear system and a desired stochastic target vector are minimal. In many cases the loss function u is convex and the occuring random variables have, at least approximately, a joint discrete distribution. Concrete problems of this type are stochastic linear programs with recourse, portfolio optimization problems, error minimization and optimal design problems. In solving stochastic optimization problems of this type by standard optimization software, the main difficulty is that the objective function F and its derivatives are defined by multiple integrals. Hence, one wants to omit, as much as possible, the time-consuming computation of derivatives of F. Using the special structure of the problem, the mathematical foundations and several concrete methods for the computation of feasible descent directions, in a certain part of the feasible domain, are presented first, without any derivatives of the objective function F. It can also be used to support other methods for solving discretely distributed stochastic programs, especially large scale linear programming and stochastic approximation methods |
| Beschreibung: | 1 Online-Ressource (XIV, 183 p. 1 illus) |
| ISBN: | 9783662025581 |
| DOI: | 10.1007/978-3-662-02558-1 |
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| 520 | |a In engineering and economics a certain vector of inputs or decisions must often be chosen, subject to some constraints, such that the expected costs arising from the deviation between the output of a stochastic linear system and a desired stochastic target vector are minimal. In many cases the loss function u is convex and the occuring random variables have, at least approximately, a joint discrete distribution. Concrete problems of this type are stochastic linear programs with recourse, portfolio optimization problems, error minimization and optimal design problems. In solving stochastic optimization problems of this type by standard optimization software, the main difficulty is that the objective function F and its derivatives are defined by multiple integrals. Hence, one wants to omit, as much as possible, the time-consuming computation of derivatives of F. Using the special structure of the problem, the mathematical foundations and several concrete methods for the computation of feasible descent directions, in a certain part of the feasible domain, are presented first, without any derivatives of the objective function F. It can also be used to support other methods for solving discretely distributed stochastic programs, especially large scale linear programming and stochastic approximation methods | ||
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| edition | 1st ed. 1988 |
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| index_date | 2024-07-03T15:15:35Z |
| indexdate | 2024-07-10T08:56:07Z |
| institution | BVB |
| isbn | 9783662025581 |
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| spelling | Marti, Kurt Verfasser aut Descent Directions and Efficient Solutions in Discretely Distributed Stochastic Programs by Kurt Marti 1st ed. 1988 Berlin, Heidelberg Springer Berlin Heidelberg 1988 1 Online-Ressource (XIV, 183 p. 1 illus) txt rdacontent c rdamedia cr rdacarrier Lecture Notes in Economics and Mathematical Systems 299 In engineering and economics a certain vector of inputs or decisions must often be chosen, subject to some constraints, such that the expected costs arising from the deviation between the output of a stochastic linear system and a desired stochastic target vector are minimal. In many cases the loss function u is convex and the occuring random variables have, at least approximately, a joint discrete distribution. Concrete problems of this type are stochastic linear programs with recourse, portfolio optimization problems, error minimization and optimal design problems. In solving stochastic optimization problems of this type by standard optimization software, the main difficulty is that the objective function F and its derivatives are defined by multiple integrals. Hence, one wants to omit, as much as possible, the time-consuming computation of derivatives of F. Using the special structure of the problem, the mathematical foundations and several concrete methods for the computation of feasible descent directions, in a certain part of the feasible domain, are presented first, without any derivatives of the objective function F. It can also be used to support other methods for solving discretely distributed stochastic programs, especially large scale linear programming and stochastic approximation methods Operations Research/Decision Theory Economic Theory/Quantitative Economics/Mathematical Methods Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Mathematical and Computational Engineering Operations research Decision making Economic theory System theory Calculus of variations Applied mathematics Engineering mathematics Diskrete Verteilung (DE-588)4150183-4 gnd rswk-swf Diskrete Wahrscheinlichkeitsverteilung (DE-588)4150184-6 gnd rswk-swf Stochastische Optimierung (DE-588)4057625-5 gnd rswk-swf Diskrete Wahrscheinlichkeitsverteilung (DE-588)4150184-6 s Stochastische Optimierung (DE-588)4057625-5 s DE-604 Diskrete Verteilung (DE-588)4150183-4 s Erscheint auch als Druck-Ausgabe 9783540187783 Erscheint auch als Druck-Ausgabe 9783662025598 https://doi.org/10.1007/978-3-662-02558-1 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Marti, Kurt Descent Directions and Efficient Solutions in Discretely Distributed Stochastic Programs Operations Research/Decision Theory Economic Theory/Quantitative Economics/Mathematical Methods Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Mathematical and Computational Engineering Operations research Decision making Economic theory System theory Calculus of variations Applied mathematics Engineering mathematics Diskrete Verteilung (DE-588)4150183-4 gnd Diskrete Wahrscheinlichkeitsverteilung (DE-588)4150184-6 gnd Stochastische Optimierung (DE-588)4057625-5 gnd |
| subject_GND | (DE-588)4150183-4 (DE-588)4150184-6 (DE-588)4057625-5 |
| title | Descent Directions and Efficient Solutions in Discretely Distributed Stochastic Programs |
| title_auth | Descent Directions and Efficient Solutions in Discretely Distributed Stochastic Programs |
| title_exact_search | Descent Directions and Efficient Solutions in Discretely Distributed Stochastic Programs |
| title_exact_search_txtP | Descent Directions and Efficient Solutions in Discretely Distributed Stochastic Programs |
| title_full | Descent Directions and Efficient Solutions in Discretely Distributed Stochastic Programs by Kurt Marti |
| title_fullStr | Descent Directions and Efficient Solutions in Discretely Distributed Stochastic Programs by Kurt Marti |
| title_full_unstemmed | Descent Directions and Efficient Solutions in Discretely Distributed Stochastic Programs by Kurt Marti |
| title_short | Descent Directions and Efficient Solutions in Discretely Distributed Stochastic Programs |
| title_sort | descent directions and efficient solutions in discretely distributed stochastic programs |
| topic | Operations Research/Decision Theory Economic Theory/Quantitative Economics/Mathematical Methods Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Mathematical and Computational Engineering Operations research Decision making Economic theory System theory Calculus of variations Applied mathematics Engineering mathematics Diskrete Verteilung (DE-588)4150183-4 gnd Diskrete Wahrscheinlichkeitsverteilung (DE-588)4150184-6 gnd Stochastische Optimierung (DE-588)4057625-5 gnd |
| topic_facet | Operations Research/Decision Theory Economic Theory/Quantitative Economics/Mathematical Methods Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Mathematical and Computational Engineering Operations research Decision making Economic theory System theory Calculus of variations Applied mathematics Engineering mathematics Diskrete Verteilung Diskrete Wahrscheinlichkeitsverteilung Stochastische Optimierung |
| url | https://doi.org/10.1007/978-3-662-02558-1 |
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