(2) Consider the quadratic objective function f (x, y) = 2x2 + y2 2xy - 8x + 2y + 10 whose contour plot is given on the next page. The contours there are [0.1, 0.5, 1, 2, 4, 6, 8, 12, 16, 20, 24). (a) Beginning at the point Xo = (-2,-2), apply the method of steepest descent with exact line search to find the next 2 points of the iteration (i.e., up to x2). Do this analytically (i.e., exactly) and plot these points on the contour plot. Then plot several more points (by sketch alone) until you are close to the optimal point. (b) Beginning with the point 30 (-2,-2) and seed direction go do (0,1), apply the conjugate gradient method until the optimal point is reached. Do this analytically i.e., exactly) and plot the points 10, 11, ... along with the conjugate directions do, d1, .... (c) Beginning with the point Xo = (-2,-2) and seed direction go = do(0,1), apply the method of coordinate descent until close to the optimal point. Do the calculations exactly for the first 2 points, but just sketch the remaining points. 2. 3 3 (2) Consider the quadratic objective function f (x, y) = 2x2 + y2 2xy - 8x + 2y + 10 whose contour plot is given on the next page. The contours there are [0.1, 0.5, 1, 2, 4, 6, 8, 12, 16, 20, 24). (a) Beginning at the point Xo = (-2,-2), apply the method of steepest descent with exact line search to find the next 2 points of the iteration (i.e., up to x2). Do this analytically (i.e., exactly) and plot these points on the contour plot. Then plot several more points (by sketch alone) until you are close to the optimal point. (b) Beginning with the point 30 (-2,-2) and seed direction go do (0,1), apply the conjugate gradient method until the optimal point is reached. Do this analytically i.e., exactly) and plot the points 10, 11, ... along with the conjugate directions do, d1, .... (c) Beginning with the point Xo = (-2,-2) and seed direction go = do(0,1), apply the method of coordinate descent until close to the optimal point. Do the calculations exactly for the first 2 points, but just sketch the remaining points. 2. 3 3