course: Numerical Analysis

pleae a&b

8. Consider this constrained minimization problem : Minimize fx,y) = x+y subject to g(x, y) = (x-1) + (y-1) = 1 A geometric solution is described below. ?T v maximizer at (1+web, H.) (x-1)+7-1)=/ k minimizer at (1-, 1-E) Use Courant's penalty method as follows: Let Fn (x, y) = f(x, y) + 1 (g(x, y))* la) Find (Xn, yn) that minimizes Fn (x,y). 16) Let X = nog (xn, Yn) and x = lim da Find An and a where we also have of (Xmin, Ymin) td og LXmin, Ymin) = 0. noo 8. Consider this constrained minimization problem : Minimize fx,y) = x+y subject to g(x, y) = (x-1) + (y-1) = 1 A geometric solution is described below. ?T v maximizer at (1+web, H.) (x-1)+7-1)=/ k minimizer at (1-, 1-E) Use Courant's penalty method as follows: Let Fn (x, y) = f(x, y) + 1 (g(x, y))* la) Find (Xn, yn) that minimizes Fn (x,y). 16) Let X = nog (xn, Yn) and x = lim da Find An and a where we also have of (Xmin, Ymin) td og LXmin, Ymin) = 0. noo