OPTIMIZATION - We need to do the following:

3. Dual problem Consider the optimization problem min f(1) = 2x} +r subject to 113-1 with r ER? a) (2 points) Draw a picture of the constraint-cost set S = {(g(*), f(x)): 1 R2). Mark in your picture f*. Can you conclude from the picture if a multiplier i* exists? If yes, visualize the multiplier in your picture. b) (1 point) Calculate the dual function (). c) (2 points) State and solve the dual problem. Compute q*. Is there a duality gap? Does there exist a multiplier? 3. Dual problem Consider the optimization problem min f(1) = 2x} +r subject to 113-1 with r ER? a) (2 points) Draw a picture of the constraint-cost set S = {(g(*), f(x)): 1 R2). Mark in your picture f*. Can you conclude from the picture if a multiplier i* exists? If yes, visualize the multiplier in your picture. b) (1 point) Calculate the dual function (). c) (2 points) State and solve the dual problem. Compute q*. Is there a duality gap? Does there exist a multiplier