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Machine Learning Foundations · End Term · 13 Apr 2025 · January 2025 term · Set QDD1

Question 14: Consider an optimization problem \min f(x, y, z, w) = x^…

Question 14

+3 marksNumerical answer

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.

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Correct answer: 0.25

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Question 14 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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