Median Versus Mean For a given vector v Rn, the mean can be found as the solution to the optimization problem min vx12, (1) xR where 1 is the vector of ones in Rn. Similarly, the median (any value x such that there is an equal number of values in v above or below x) can be found via xR min vx11. (2) We consider a robust version of the mean problem (1): min max v+ux1 2, (3) x u : u in which we assume that the components of v can be independently perturbed by a vector u whose magnitude is bounded by a given number 0. (a) Is the robust problem (3) convex? Justify your answer precisely, based on expression (3), and without further manipulation