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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Descent Directions and Efficient Solutions in Discretely Distributed Stochastic Programs

Descent Directions and Efficient Solutions in Discretely Distributed Stochastic Programs

Marti, Kurt

Paperback

Series: Lecture Notes in Economic and Mathematical Systems, Book 299

Business GeneralGeneral MathematicsProbability & Statistics

ISBN10: 3540187782
ISBN13: 9783540187783
Publisher: Springer
Published: Jan 27 1988
Pages: 183
Weight: 0.72
Height: 0.42 Width: 6.69 Depth: 9.61
Language: English
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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