A quadratic recourse function for the two-stage stochastic program John R. Birge, Stephen M. Pollock, and Liqun Qi.

We present a quadratic recourse representation of the two-stage stochastic linear problem. Unlike the usual linear recourse model, it is differentiable with respect to the first stage decision variables. This offers the possibility of applying high convergence rate methods to solve the two-stage problem. We show that the quadratic recourse function approximates the linear recourse function (and the corresponding solution of the two-stage problem with quadratic recourse converges to the solution of the two-stage problem with linear recourse) as a parameter k → ∞ and another parameter ɛ k → 0. We also give a bound for this approximation.

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