... the notion of theaffine hull of a convexsetX[denotedaff(X)]. This is the intersection of all hyperplanes containingX.•Therelative interior of X, denotedri(X), is the set of allx ∈ ... xi=0or1,i=1, ,n.EXAMPLES OF DISCRETE PROBLEMS•Given a directed graph with set of nodesNandset of arcs(i, j) ∈A, the (integer constrained) min-imum cost network flow problem isminimize(i,j)∈Aaijxijsubject ... andsiare given scalars.•Think of: −Nodesiwithsi> 0andsi< 0as productionand consumption points, respectively.− sisupply or demand of nodei.−Arcs(i, j)as transportation...