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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Explain the concept of gradient descent in simple terms.
💡 Hint: Think about how one would climb down a hill.
Question 2
Easy
What are Lagrange multipliers used for?
💡 Hint: Consider how to maximize or minimize with certain limitations.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is the main purpose of gradient descent?
- To maximize a function
- To minimize a function
- To find a global maximum
- None of the above
💡 Hint: It’s about finding the lowest point!
Question 2
The Lagrange multiplier method helps in managing which type of constraints?
- True
- False
💡 Hint: Think about equalities vs inequalities.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the function f(x, y) = xy and the constraint x + y = 10, use the Lagrange multiplier method to find the maximum value.
💡 Hint: Make sure to substitute back the constraint into your equations.
Question 2
Using KKT conditions, analyze the function f(x) = x^2 with the constraint x ≥ 1. Determine if there are any optimal points at the boundary.
💡 Hint: Remember, complementary slackness helps you identify active constraints.
Challenge and get performance evaluation