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

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 8
minx1,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≤1
x+2y≥2
x≥−1
Find 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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These are NPTEL Data Science for Engineers Assignment 5 Answers