PTU Punjab Technical University B-Tech May 2019 Question Papers 6th Semester Computer Science Engineering (CSE)

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Roll No.

Total No. of Pages : 03

Total No. of Questions : 18

B.Tech.(CSE) (O.E. 2011 Onwards) (Sem-6)

OPTIMIZATION TECHNIQUES

Subject Code : CH-304

M.Code : 71555

Time : 3 Hrs. Max. Marks : 60

INSTRUCTIONS TO CANDIDATES :

1.

SECTION-A is COMPULSORY consisting of TEN questions carrying T WO marks

each.

2.

SECTION-B contains FIVE questions carrying FIVE marks each and students

have to attempt any FOUR questions.

3.

SECTION-C contains T HREE questions carrying T EN marks each and students

have to attempt any T WO questions.

SECTION-A

1.

Define the property of continuity.

2.

What are the six steps used to solve optimization problem.

3.

What is constrained problem and give one example.

4.

Give the classification of optimization problems.

5.

Are the following functions continuous? (a) f (x) = 1/x and (b) f (x) = 1n (x)

6.

State disadvantages of Newton's method for one-dimensional search?

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7.

State the Kuhn-Tucker conditions.

8.

What is the difference between local optimal point and global optimal point?

9.

Is it necessary that the Hessian matrix of the objective function always be positive

definite in an unconstrained minimization problem?

10. Find two non-negative numbers whose sum is 9 and so that the product of one number

and the square of the other number is a maximum.

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SECTION-B

11. Does the following set of constraints form an convex region ?

g1(x)

2

2

(x x ) 9 0and g (x) x x 1 0

1

2

2

1

2

12. Apply golden section one dimensional search technique to reduce the interval of

uncertainty for the maximum of the function f = 6.64 + 1.2x ? x2 from [0, 1] to less than 2

percent of its original size.

13. Consider the objective function,

2

2

f (x) x 2x 3x 6x 4

1

1

2

2

Find the stationary points and classify them using the Hessian matrix.

14. Minimize f (x) = x2 ? x using Secant method, with the two points x = ? 3 and x = 3.

15. Find the dimensions of a cylindrical tin (with top and bottom) made up of a sheet metal to

maximize its volume such that the total surface area is equal to 22.

SECTION-C

16. In crystal NaCl, each Na+ or Cl? ion is surrounded by 6 nearest neighbors of opposite

charge and 12 nearest neighbors of the same charge. Two sets of forces oppose each other

: the columbic attraction and the hard-core repulsion. The potential energy u (r) of the

crystal is given by the Lennard-Jones potential expression,

12

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6

u(r) 4

where > 0, > 0 are constants.

r

r

a) Does the Lennard-Jones potential u (r) have stationary points (s)? If it does, locate it

(them).

b) Identify the nature of the stationary point(s) min, max, etc.

c) What is the magnitude of the potential energy at the stationary point(s).

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17.

Estimate the minimum of :

12

1

5

2

f (x) 3x

5 in the interval

x

.

3

x

2

2

By using Powell's method with initial point x1 = 0.5 and step size = 0.5. For

convergence use parameters

Difference in x

Difference in F

2

3

3 1

0

and

3 1

0

x

F

18. Maximize the objective function, using simplex method.

Z = 40x1 + 88x2

Subject to

2x1 + 8x2 60

5x1 + 2x2 60

x1 0

x2 0

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NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any

page of Answer Sheet will lead to UMC against the Student.

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This post was last modified on 04 November 2019