3.21 Pointuwise maximum and supremum. Show that the following functions f : R" → R are convex. (a) f(x): = max;=1,.,k ||Aª)x – b@)||, where A) e Rmxn, b(i) e R™ and || · || is a norm on R™. (b) ƒ(x) =...

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Extracted text: 3.21 Pointuwise maximum and supremum. Show that the following functions f : R" → R are convex. (a) f(x): = max;=1,.,k ||Aª)x – b@)||, where A) e Rmxn, b(i) e R™ and || · || is a norm on R™. (b) ƒ(x) = E, a|g on R", where |æ| denotes the vector with |x|; = |xi| (i.e., |x| is the absolute value of x, componentwise), and |x|f2] is the ith largest component of |x|. In other words, |æ|1], |x|(2), ..., |æ|[n] are the absolute values of the components of x, sorted in nonincreasing order.