Consider the linear program minimize f(x) = cTx subject to Ax >= b. (i) Write the first- and second-order necessary conditions for a local solution. (ii) Show that the second-order sufficiency conditions do not hold anywhere, but that any point x. satisfying the first-order necessary conditions is a global minimizer. (Hint Show that there are no feasible directions of descent at xx, and that this implies that x, is a global minimizer.)
