Descent Directions and Efficient Solutions in Discretely Distributed Stochastic Programs - Marti, Kurt

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Résumé :
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.

Biographie:
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....

Sommaire:
Dr. Kurt Marti ist Professor f?r Mathematik und Rechneranwendung an der Universit?t der Bundeswehr in M?nchen. Er ist Vorsitzender der IFIP-Arbeitsgruppe zur Stochastischen Optimierung ?und war Vorsitzender der GAMM-Special-Interest-Group Applied Stochastics and Optimization. Professor Marti ist Verfasser mehrerer deutsch- und englischsprachiger Fachb?cher zur angewandten Mathematik und zur Optimierung und hat mehr als 160 Beitr?ge in wissenschaftlichen Zeitschriften ver?ffentlicht....