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A General Stochastic Programming Problem
Authors:Yu M Yermol'yev
Abstract:Stochastic programming problems appear when we make decisions in situations with uncertainty and risk, when any action has an ambiguous outcome and to each solution x = (x1 …, xn) it is possible to associate certain indicators fi (x, ω), i = 1, …, m, that depend on x and on the state of nature ω, which is an element of the probabilistic space (Ω, A, P).

Since for any x the value of the objective function f 1 (x, ω) and of the constraints functions f(x, ω), i = 2,… m, will depend on the realization ω, we have great freedom in determining the feasible and the optimal solutions in stochastic programming problems; for example, deciding whether they should be deterministic or have random solutions.
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