Podcast
Play an AI-generated podcast conversation about this lesson
Questions and Answers
In the context of dual problems, what is the dual function for the first example?
In the context of dual problems, what is the dual function for the first example?
- $g(\mu) = -\mu^T A P A^T \mu + \mu^T b$
- $g(\mu) = \mu^T A P A^T \mu - \mu^T b$
- $g(\mu) = -\mu^T A P^{-1} A^T \mu - \mu^T b$ (correct)
- $g(\mu) = -\mu^T P A A^T \mu - \mu^T b$
What is the optimal dual variable for the first example?
What is the optimal dual variable for the first example?
- $\mu^* = 2 A P A^T b$
- $\mu^* = -2 A P A^T b$
- $\mu^* = 2 A P^{-1} A^T b$
- $\mu^* = -2 A P^{-1} A^T b$ (correct)
What is the dual function for the second example?
What is the dual function for the second example?
- $g(\lambda) = -\lambda^T P B B^T \lambda - \lambda^T c$
- $g(\lambda) = -\lambda^T B P^{-1} B^T \lambda - \lambda^T c$ (correct)
- $g(\lambda) = \lambda^T B P B^T \lambda - \lambda^T c$
- $g(\lambda) = -\lambda^T B P B^T \lambda + \lambda^T c$
What condition ensures that the maximum value of the dual problem equals the minimum value of the original problem in the second example?
What condition ensures that the maximum value of the dual problem equals the minimum value of the original problem in the second example?
Signup and view all the answers
What is used to express the strong duality in both examples?
What is used to express the strong duality in both examples?
Signup and view all the answers
