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2023-24 Second Semester
AI4003 Optimization in ML
Assignment 4
Due Date: 20/May/2024(Mon), before 10:00pm.
• Write down your Chinese name and student number. Write neatly on A4-sized paper and show your steps.
• Late submissions or answers without details will not be graded.
1. Answer the questions:
(a) What is the feasible set in constrained optimization?
(b) How to convert inequality constriant into equality constraint?
2. For the following primal problem, ffnd the dual problem
min f(x, y) = 5x + 6y
s.t.3x + 2y ≥ 10
4x + 7y≥ 9
where x and y are positive.
3. [Lagrangian] Find the minimum of the function
f(x, y) = x
2 + (y − 1)
2
s.t.x + 2y = 2
4. Maximum entropy distributions under moment constraints.
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