... λ,1) CONVEXITY Convex Sets Nonconvex Sets x y αx + (1 - α)y, 0 < α < 1 x x y y x y Convex and nonconvex sets. αf(x) + (1 - α)f(y) xy C z f(z) A convex function. Linear interpolation underestimates ... EQUALITY CONSTRAINTS • Suppose we have the additional constraints e i x − d i =0,i=1, ,m • We need the notion of the affine hull of a convex set X [denoted aff(X) ]. This is the intersection of all ... PROGRAMMING • Enumeration of the finite set of all feasible (in- teger) solutions, and comparison to obtain an op- timal solution (this is rarely practical). • Constraint relaxation and heuristic rounding....