Stochastic Programming Problems with Recourse via Empirical Estimates
نویسنده
چکیده
Let ξ := ξ(ω) (s×1) be a random vector defined on a probability space (Ω, S, P ); F, PF the distribution function and the probability measure corresponding to the random vector ξ. Let, moreover, g0(x, z), g1 0(y, z) be functions defined on Rn × Rs and Rn1 × Rs; fi(x, z), gi(y), i = 1, . . . , m functions defined on Rn × Rs and Rn1 ; h := h(z) (m × 1) a vector function defined on Rs, h ′ (z) = (h1(z), . . . , hm(z)); X ⊂ Rn, Y ⊂ Rn1 be nonempty sets. Symbols x (n× 1), y := y (x, ξ) (n1 × 1) denote decision vectors. (Rn denotes the n–dimensional Euclidean space, h ′ a transposition of the vector function h.) Stochastic programming problems with recourse (in a rather general setting) can be introduced as the following problem: Find
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