## NPTEL Data Science for Engineers Week 5 Assignment Answers 2024

1. Which of the following statements is/are not TRUE with respect to the multi variate optimization?

I – The gradient of a function at a point is parallel to the contours

II – Gradient points in the direction of greatest increase of the function

III – Negative gradients points in the direction of the greatest decrease of the function

IV – Hessian is a non-symmetric matrix

- I
- II and III
- I and IV
- III and IV

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2. The solution to an unconstrained optimization problem is always the same as the solution to the constrained one.

- True
- False

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3. Gradient based algorithm methods compute

- only step length at each iteration
- both direction and step length at each iteration
- only direction at each iteration
- none of the above

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Answer :-

5. Which among the following is the stationary point for f(x_{1},x_{2})?

- (0, 0)
- (1, −1)
- (−1, −1)
- (−1, 1)

Answer :-

6. Find the eighen values corresponding to Hessian matrix of *f*.

- 1, −1
- 1, 1
- 2, 8
- 0, 2

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7. Find the minimum value of *f*.

- 0
- −5
- −1
- 1

Answer :-

Answer :-

9. What is the minimum value of *f*(x_{1},x_{2}) subject to the above mentioned constrained?

- −5
- −1
- 27
- 0

Answer :-

10. Find the maximum value of* f*(x,y)=49−x^{2}−y^{2} subject to the constraints x+3y=10.

- 49
- 46
- 59
- 39

Answer :-

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