Optimization

90 Optimization: Algorithms and Applications

11. Minimize the function

f x x( )x = +

( )

1

2

8

1

2

2

2

from the starting point (1, 2) using the steepest descent method.

Observe the sluggishness of this method. Again, solve the function

by the conjugate gradient method and compare the performance

with the steepest descent method.

12. A manufacturing rm wants to divide its resources suitably between

capital (x

1

) and labor (x

2

) so as to maximize the prot function given by

f(x) = p{ln(1 + x

1

) + ln(1 + x

2

)} − wx

2

− vx

1

where p is the unit price of the product, w is the wage rate of labor,

and v is the unit cost of capital.

i. ...