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Descent Directions and Efficient Solutions in Discretely Distributed Stochastic Programs: 299 (Lecture Notes in Economics and Mathematical Systems, 299) - Softcover

Marti, Kurt

 
9783540187783: Descent Directions and Efficient Solutions in Discretely Distributed Stochastic Programs: 299 (Lecture Notes in Economics and Mathematical Systems, 299)
Softcover
ISBN 10: 3540187782 ISBN 13: 9783540187783
Publisher: Springer, 1988

Synopsis

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.

"synopsis" may belong to another edition of this title.

About the Author

Prof. Dr. Kurt Marti is a Professor Emeritus of Engineering Mathematics at the Federal Armed Forces University in Munich, Germany. He is a former Chairman of IFIP Working Group 7.7 "Stochastic Optimization" and a former Chairman of the GAMM Special Interest Group "Applied Stochastics and Optimization". Professor Marti has published several books, both in German and in English, and more than 160 papers in refereed journals.

From the Back Cover

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.

"About this title" may belong to another edition of this title.

Publisher
Springer
Publication date
1988
Language
English
ISBN 10 
3540187782
ISBN 13 
9783540187783
Binding
Paperback
Number of pages
183