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*L*-shaped Method for Two-stage Stochastic Programs with RecourseThis is the free portion of the full article.
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*L*-shaped Method for Two-stage Stochastic Programs with Recourse

### Article Outline

Keywords

*L*-Shaped Method for Two-Stage Stochastic Program with Bounded, Complete Recourse

See also

References

Keywords Stochastic programming - Recourse - Decomposition techniques

A

where ,

and denotes the mathematical expectation with respect to ξ,

*stochastic linear program with recourse*( SLP) is a mathematical program of the form*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*)