Quiz Space

Machine Learning Foundations · End Term · 13 Apr 2025 · January 2025 term · Set QDD3

Question 12: Consider an optimization problem \min f(x, y, z, w) = x^…

Question 12

+2 marksOne or more correct options

Consider an optimization problem

min⁡f(x,y,z,w)=x2+y2+z2+w2+1\min f(x, y, z, w) = x^2 + y^2 + z^2 + w^2 + 1

subject to constraints:

x+y+z+w=1x + y + z + w = 1

w≤δw \le \delta

Let the Lagrangian function is,

L(x,α,β)=x2+y2+z2+w2+1+α(1−x−y−z−w)+β(w−δ)L(x, \alpha, \beta) = x^2 + y^2 + z^2 + w^2 + 1 + \alpha(1 - x - y - z - w) + \beta(w - \delta)

Based on the above data, answer the given subquestions.

Which of the following statements correctly represent the Karush-Kuhn-Tucker (KKT) conditions for the given optimization problem?

Select all that apply.

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answers

  • A
  • C
See the whole paperTake it as a mock test

Question 12 of 14 in the IIT Madras BS Machine Learning Foundations (MLF) End Term paper sat on 13 Apr 2025, in the January 2025 term (IIT M DIPLOMA AN EXAM QDD3 13 Apr 2025). It carries 2 marks.

More questions from this paper

  1. Q1Figure question
  2. Q2The random variable y is being transformed according to the measurement mapping: z = Cy + \epsilon, where: z \in \mathb…
  3. Q3Which of the following statements about singular value decomposition (SVD) is/are true?
  4. Q4In the context of Linear Algebra, which of the following statements about Principal Component Analysis (PCA) is/are tru…
  5. Q5Which of the following options is/are true?
  6. Q6Which of the following options is/are true ?
  7. Q7Figure question
  8. Q8Figure question
  9. Q9Figure question
  10. Q10Figure question
  11. Q11Figure question
  12. Q13Consider an optimization problem \min f(x, y, z, w) = x^2 + y^2 + z^2 + w^2 + 1 subject to constraints: x + y + z + w =…
  13. Q14Consider an optimization problem \min f(x, y, z, w) = x^2 + y^2 + z^2 + w^2 + 1 subject to constraints: x + y + z + w =…