Recent Results in Stochastic Programming -

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Résumé :
This vo1ume contains most of the papers (two of the~ as extended abstracts) presented at a meeting on stochastic programming, held at Oberwolfach, January 28 - February 3, 1979. A1though the number of participants had to be small for technical rea? sons, the area covered by the 1ectures during the meeting was rather broad. lt contains fundamental theoretical problems - e.g. continuity in parametric programming, optima1ity conditions and decision rules for stochastic programming problems and convexity statements also nee? ded for chance constrained problems - as well as very important prac? tical problems, as computational methods for various models and appli? cations to water storage problems, dynamic inventory control, asphalt mixing, portfolio selection, and so on. Without any doubt there are still many theoretical and computational problems of this field unso1ved, and some of them can be discovered in this volume. On the other hand, the papers presented here also show, that during the last two decades knowledge - theoretical and computa? tional - on stochastic programming, and practical experience with it, have been developped so far, that neglecting apriori the stochastic nature of parameters for almost every price - very often done in mo? delling a practical decision situation as deterministic optimization problem - can no longer be justified.

Sommaire:
I. Theoretical Results.- Stochastic-Parametric Linear Programs II.- A Necessary Condition for Continuity in Parametric Linear Programming.- On Parametric Linear Optimization IV. Differentiable Parameter Functions.- Conditions for Optimality in Multi-Stage Stochastic Programming Problems.- A Note on Sequential Minimax Rules for Stochastic Linear Programs.- A Dual of a Dynamic Inventory Control Model: The Deterministic and Stochastic Case.- Convexity and Optimization in Certain Problems in Statistics.- II. Applications and Methods.- Computation of Multiple Normal Probabilities.- Water Resources System Modelling Using Stochastic Programming with Recourse.- Solving Complete Fixed Recourse Problems by Successive Discretization - Extended Abstract -.- An Extended Frank-Wolfe Algorithm with Application to Portfolio Selection Problems.- Duality in Stochastic Programming Applied to the Design and Operation of Reservoirs.- Chance Constrained Inventory Model for an Asphalt Mixing Problem.- Solving Stochastic Linear Programs by Semi-Stochastic Approximation Algorithms.- Network Planning Using Two-Stage Programming under Uncertainty....