Engineering Optimization: Theory and Practice, Fourth Edition

118 Classical Optimization Techniques

subject to

x 22 −x 1 ≥ 0

x 12 −x 2 ≥ 0

−^12 ≤x 1 ≤^12 , x 2 ≤ 1

X 1 =

{

0

0

}

, X 2 =

{

0

− 1

}

, X 3 =

{

−^12

1

4

}

2.76 Consider the following optimization problem:

Minimizef= −x 12 −x^22 +x 1 x 2 + 7 x 1 + 4 x 2

subject to

2 x 1 + 3 x 2 ≤ 24

− 5 x 1 + 12 x 2 ≤ 24

x 1 ≥ 0 , x 2 ≥ 0 , x 2 ≤ 4

Find a usable feasible direction at each of the following design vectors:

X 1 =

{

1

1

}

, X 2 =

{

6

4

}