Adaptive discretization of convex multistage stochastic programs

min x FI(x,ξ) := ∑ i∈I pi f (xi,ξi) s.t. gt(n)(x 1, . . . ,xn,ζn) ≤ 0, xn ∈ Xt(n), n ∈ N(I) f (x,ξ), gt(x,ξ) convex in x, Xt convex, t = 1, . . . ,T Notation ξi i ∈ I scenarios of stoch. process ξ ξn := ξi,t(n) ζn := (ξ1, . . . ,ξn) xi i ∈ I decision vector for scenario i xn := xi,t(n) pi i ∈ I scenario probabilities N(I) nodes of scenario tree defined by scenarios in I t(n) timestage of node n T number of timestages