Duality Problems in Quadratic Programming
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Questions and Answers

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?

  • $\mu^* = 2 A P A^T b$
  • $\mu^* = -2 A P A^T b$
  • $\mu^* = 2 A P^{-1} A^T b$
  • $\mu^* = -2 A P^{-1} A^T b$ (correct)
  • What is the dual function for the second example?

  • $g(\lambda) = -\lambda^T P B B^T \lambda - \lambda^T c$
  • $g(\lambda) = -\lambda^T B P^{-1} B^T \lambda - \lambda^T c$ (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?

    <p>Slater's condition</p> Signup and view all the answers

    What is used to express the strong duality in both examples?

    <p>$d = g(\mu^<em>) = f(x^</em>) = p^*$</p> Signup and view all the answers

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