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

Question 13: Consider an optimization problem \min f(x, y, z, w) = x^…

Question 13

+3 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 are correct based on the KKT conditions and the solution to the optimization problem?

Select all that apply.

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

Correct answers

  • A
  • C
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Question 13 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 3 marks.

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