6. (14%) Let 01,02,. . .,cm be m distinct vectors in R\

6. (14%) Let Cl,C2,..., m c problem (P): be m distinct vectors in R n, with m 2 2. Consider the primal Minimize subject to 2 Ilx Ci112 z for i = where II II is the O-norm. (a) Formulate and compute its Lagrangian dual (D). (1, O)T, and c2 = (O, I)T. Let D = (0.25, 0.25)T. Find (b) Assume that m = n = 2, Cl = its corresponding solution (i, E) to (P). Is it true that is an optimal solution to (D) and (i, 2) is an optimal solution to (P)? Justify your answer rigorously.