1. (30 points) Consider the following minimization problem: f(x, y, z) = 22 + y2 + z2 ty 2z+yz+x - 3y - 22+4 (a) Find the global minimizer and the optimal objective functional value analytically. (b) Alternatively, we consider the numerical approach. With an initial guess of [x",y, z0j? = [0,0,0)", perform one iteration of the steepest de- scent algorithm. Show all the computational steps. (e) With an initial guess of [z(), y), z(0)]? = [a, b, c" (where a, b, c are the last three digits of your student ID number), perform one iteration of the Newton's method. Show all the computational steps. 1. (30 points) Consider the following minimization problem: f(x, y, z) = 22 + y2 + z2 ty 2z+yz+x - 3y - 22+4 (a) Find the global minimizer and the optimal objective functional value analytically. (b) Alternatively, we consider the numerical approach. With an initial guess of [x",y, z0j? = [0,0,0)", perform one iteration of the steepest de- scent algorithm. Show all the computational steps. (e) With an initial guess of [z(), y), z(0)]? = [a, b, c" (where a, b, c are the last three digits of your student ID number), perform one iteration of the Newton's method. Show all the computational steps