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L-shaped Method for Two-stage Stochastic Programs with Recourse

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L-Shaped Method for Two-Stage Stochastic Program with Bounded, Complete Recourse
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Keywords Stochastic programming - Recourse - Decomposition techniques

A stochastic linear program with recourse ( SLP) is a mathematical program of the form
where ,
and denotes the mathematical expectation with respect to ξ, x is an (n 1 × 1) decision vector, and for each ξ, y is (n 2 × 1). A is (m 1 × n 1) and for each ξ, h is (m 2 × 1). All other matrices and vectors have conformable dimensions. Transposes are omitted for simplicity. The random vector ξ is formed by the random components of q, h and T · Q(x, ξ) is the second-stage value function for a given ξ and Q(x) the expected value-function or expected recourse.
In the case where random vectors are described by discrete distributions, Q(x)