Consider the problem of maximizing cx subject to ! j ajx2 j ≤ b, where each aj > 0 and b > 0, and xj is any real number. (a) Solve the problem by applying KKT conditions. (b) Solve the Lagrangean...

Consider the problem of maximizing cx subject to !

j ajx2

j ≤ b, where

each aj > 0 and b > 0, and xj is any real number. (a) Solve the problem by

applying KKT conditions. (b) Solve the Lagrangean dual. Show that there is

no duality gap, and that the optimal dual solution u is identical to the vector

μ of Lagrange multipliers that satisfies the KKT conditions. Hint: For part

(a), note that g(x) is convex.