# Data Science for Engineers | Week 5

**Course Name: Data Science for Engineers**

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**These are NPTEL Data Science for Engineers Assignment 5 Answers**

**Q1. 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 gradient points in the direction of the greatest decrease of the function

IV – Hessian is a non-symmetric matrix

a. I

b. II and III

c. I and IV

d. III and IV

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 gradient points in the direction of the greatest decrease of the function

IV – Hessian is a non-symmetric matrix

**Answer: c. I and IV**

**Q2. The solution to an unconstrained optimization problem is always the same as the solution to the constrained one.**

a. True

b. False

**Answer: b. False**

**These are NPTEL Data Science for Engineers Assignment 5 Answers**

**Q3. Gradient based algorithm methods compute**

a. only step length at each iteration

b. both direction and step length at each iteration

c. only direction at each iteration

d. none of the above

**Answer: b. both direction and step length at each iteration**

**Q4. For an unconstrained multivariate optimization given f(x¯¯¯), the necessary second order condition for x¯¯¯∗ to be the minimizer of f(x) is**

a. ∇2f(x¯¯¯∗) must be negative definite.

b. ∇2f(x¯¯¯∗) must be positive definite.

c. ∇f(x¯¯¯∗)=0

d. f”(x¯¯¯∗)>0

**Answer: b. ∇2f(x¯¯¯∗) must be positive definite.**

**These are NPTEL Data Science for Engineers Assignment 5 Answers**

**Use the following information to answer Q5, 6, 7 and 8minx1,x2∈R f(x1,x2)=x21+4×22−2×1+8×2.**

**Q5. Which among the following is the stationary point for f(x1,x2)?**

a. (0,0)

b. (1,−1)

c. (−1,−1)

d. (−1,1)

**Answer: b. (1,−1)**

**Q6. Find the eigen values corresponding to Hessian matrix of f.**

a. 1,−1

b. 1,1

c. 2,8

d. 0,2

**Answer: c. 2,8**

**These are NPTEL Data Science for Engineers Assignment 5 Answers**

**Q7. Find the minimum value of f.**

a. 0

b. −5

c. −1

d. 1

**Answer: b. −5**

**Q8. What is the minimum value of f(x1,x2)csubject to the constraint x1+2×2=7?**

a. −5

b. −1

c. 27

d. 0

**Answer: c. 27**

**These are NPTEL Data Science for Engineers Assignment 5 Answers**

**Q9. Find the maximum value of f(x,y)=49−x2−y2 subject to the constraint x+3y=10.**

a. 49

b. 46

c. 59

d. 39

**Answer: d. 39**

**Q10. Consider an optimization problem minx1,x2 x2−xy+y2 subject to the constraints 2x+y≤1x+2y≥2x≥−1Find the lagrangian function for the above optimization problem.**

a. L(x,y,µ1,µ2,µ3)=x2−xy+y2+µ1(2x+y−1)+µ2(2−x−2y)+µ3(−x−1)

b. L(x,y,µ1,µ2,µ3)=x2−xy+y2+µ1(2x+y−1)+µ2(x+2y−2)+µ3(−x−1)

c. L(x,y,µ1,µ2,µ3)=x2−xy+y2+µ1(2x+y−1)+µ2(x+2y−2)+µ3(x+1)

d. L(x,y,µ1,µ2,µ3)=x2−xy+y2+µ1(1−2x−y)+µ2(2−x−2y)+µ3(−x−1)

**Answer: c. L(x,y,µ1,µ2,µ3)=x2−xy+y2+µ1(2x+y−1)+µ2(x+2y−2)+µ3(x+1)**

**These are NPTEL Data Science for Engineers Assignment 5 Answers**

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**These are NPTEL Data Science for Engineers Assignment 5 Answers**

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