Kurt Marti

Descent Directions and Efficient Solutions in Discretely Distributed Stochastic Programs (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

---

Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, B, BG, CY, CZ, D, DK, EW, E, FIN, F, GR, HR, H, IRL, I, LT, L, LR, M, NL, PL, P, R, S, SLO, SK ausgeliefert werden.

Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 183
• Erscheinungstermin: 11. November 2013
• Englisch
• ISBN-13: 9783662025581
• Artikelnr.: 52971568

Autorenporträt

Kurt Marti is a Professor of Engineering Mathematics at the University of Bundeswehr Munich. He has been Chairman of the IFIP-Working Group 7.7 on "Stochastic Optimization" and Chairman of the GAMM-Special Interest Group "Applied Stochastics and Optimization". Professor Marti has published several books, both in German and in English and he is author of more than 160 papers in refereed journals and book chapters.

Inhaltsangabe

Contents: Stochastic programs with a discrete distribution.- Stochastic dominance (SD) and the construction of feasible descent directions.- Convex programs for solving (3.1)-(3.4a),(3.5).- Stationary points (efficient solutions) of (SOP).- Optimal solutions of (Px,D),(Px,D).- Optimal solutions (y ,T ) of (Px,D) having Tij0 for all i S,j R.- Existence of solutions of the SD-conditions (3.1.)-(3.5), (12.1)-(12.5), resp; Representation of stationary points.- Construction of solutions (y,T) of (12.1)-12.4) by means of formula (44).- Construction of solutions (y,B) of (46) by using representation (60) of (A( ),b( )),- References.- Index.