Groupe d’études et de recherche en analyse des décisions

G-92-22

A Scenario Aggregation Algorithm for the Solution of Stochastic Dynamic Minimax Problems

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In this paper, we present a scenario aggregation algorithm for the solution of the dynamic minimax problem in stochastic programming. We consider the case where the joint probability distribution has a known finite support. The algorithm applies the Alternating Direction of Multipliers Method on a reformulation of the minimax problem using a double duality framework. The problem is solved by decomposition into scenario sub-problems, which are deterministic multi-period problems. Convergence properties are deduced from the Alternating Direction of Multipliers. The resulting algorithm can be seen as an extension of Rockafellar and Wets Progressive Hedging algorithm to the dynamic minimax context.

, 27 pages

Ce cahier a été révisé en janvier 1995