No. of Pages: 2

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
SECOND SEMESTER M.TECH DEGREE EXAMINAFION, APR-MAY 201 8

Mechanical Engineering

(Machine Design)

01ME6122 Optimization Techniques for Engi eering.
Max. Marks: 60 161: 3 Hours

Instructions: For search methods wherever applicable, conduct three iterations for single variable
and two iterations for multi variable optimization.

Answer ANY TWO questions from each part.

PART-A
1. Find the extremum ofthe function f (xl,xz) —~ 16×1 + 12X2 XI X2 and state weather
this point is maximum, minimum or saddle point.

(9 marks) 2. a) Discuss convex set with an example.

(3
marks)
b) Comment on the definiteness and convexity of the following
function: f 00൧൩ = 2x? — 3x1x2 + 2x2?
(6
marks)

3. Minimize f 00൧൨൧ = 4x1? + 5x} subject to 2x1 + 3x2 — 6 = 0 using Lagrangian

multipliers.
(9
marks)
PART-B
4. a) State the rules for region elimination in single variable optimization.
(3
marks)

0) Minimize f(x) = 10 + x -- 2x — 5exp(x) in the interval (-5, 5) using golden section

method.
(6
marks)
5. a) State advantages and limitations of gradient based methods.
(3mark
5) b) Minimize f(x) = exp(x) — x 3in the interval (-2, 5) using secant method.
(6

marks)