Homework 5 Spring 2014 Solutions - Math 408 Homework Set...

This preview shows page 1 - 4 out of 4 pages.

Math 408Homework Set 5(1) Consider the linearly constrained quadratic optimization problemQ(H, g, A, b)minimize12xTHx+gTxsubject toAx=b ,whereHRn×nis symmetric an positive definite andARm×nhas rank (A) =m.(a) Write necessary and sufficient optimality conditions for this problem at a pair (¯x,¯y)Rn×Rmwhere ¯yis an Lagrange multiplier vector.
1
(c) Solve the problemQ(H, g, A, b) withg= 0,m= 1,b=μR, andA=1Tn, where1nRnis the vector of all ones.Solution
(d) Show that the matrixAHATis invertible.
=[H(AH-1AT)-1AH-1-(AH-1AT)-1

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture