# Stochastic Two-Stage Programming by Dr. Karl Frauendorfer (auth.)

~ (inf 'Jfv ) = inf 'Jf . 3). 4) becomes difficult if some subsequence {'Jfv k } exists whose minimizers do not accumulate and no bounded set covering at least some minimizers of almost all approximates, no monotonicity of the inf-values respectively, is at hand. 3 : Suppose 'V is lower semicontinuous on Rn. Let {'Vv; v=1,2, ... } be a collection of functions converging pointwise to 'V. Then {'Vv; v=1,2, ...

E. q(ll)=q); moreover, we have convexity in (~,x) if the technology matrix is deterministic (T(~)=T), too. On the other hand p(ll,~,x) reduces to a saddle function in (ll,x) if both hand T are fixed (h(~)=h, T(~)=T ). In all these cases, piecewise linearity in the random arguments and in x still holds. e. W=(I,-I)) with deterministic T and q. 2) yields the following recourse function: m' p(~,x) := 2.. 1) j=! 2) yt'Yj-~O. Due to the gained separability of the recourse function in the components of ~, it suffices to consider m' one-dimensional marginal distributions of P, denoted with We then get for the objective of the Pj U=l, ...