# Nonlinear Programming: Self Test Questions

#### Theory

1. Write short notes on the following:

• Nonlinear programming
• Separable programming

2. Give the mathematical formulation of a general nonlinear programming problem.

#### Practical

1. Maximize f(x) = 2x1 + 4x2 –x12 – x22

subject to
x1 + 4x2 ≤ 5
2x1 + 3x2 ≤ 6

x1, x2 ≥ 0.

2. Maximize f(x) = x1 + x2+ x3 - 1/2(x12 + x22 + x32)

subject to
x1 + x2 + x3 ≤ 1
4x1 + 2x2 ≤ 7/3

x1, x2, x3 ≥ 0.

3. Maximize 2x1x2+ 4x2 - x22 - 2x12

subject to
x1 + 4x2 ≤ 12

x1, x2 ≥ 0.

4. Maximize 6x1 + 4x2+ 2x3 - 3x12 - 2x22 - 1/3x32

subject to
x1 + 2x2 + x3 ≤ 4

x1, x2, x3 ≥ 0.

Solve the following nonlinear programming problem by separable programming method:

1. Maximize f0 = 2x1 – x12 + x2

subject to
f1 = 2x12 + 3x22 ≤ 6
f2 = x1 ≤ 2
f3 = x2 ≤ 2

x1, x2 ≥ 0.

Take the break points of both x1 and x2 as 0, 1, 2, 3, 4.

2. Minimize x12- 4x1 + x22 - 2x3

subject to
x1 + x2 + x3 ≤ 2
(x1 + 1) x2 ≥ 2

x1, x2, x3 ≥ 0.

Take breakpoints of x1 and x2 as 0, 1, 2. Keep x3 unchanged.