Engineering Optimization: Theory and Practice, Fourth Edition

96 Classical Optimization Techniques

Figure 2.8 Feasible directionS.

Example 2.12 Consider the following optimization problem:

Minimizef (x 1 , x 2 )=x 12 +x^22

subject to

x 1 + 2 x 2 ≤ 51

1 ≤xi≤ 01 ;i= 1 , 2

Derive the conditions to be satisfied at the pointX 1 = { 1 , 7 }Tby the search direction

S={s 1 , s 2 }Tif it is a (a) usable direction, and (b) feasible direction.

SOLUTION The objective function and the constraints can be stated as

f (x 1 , x 2 )=x^21 +x 22

g 1 (X)=x 1 + 2 x 2 ≤ 51