Consider the problem of minimizing the sum of squared residuals subject to the constraint that Rb r, where R is q (k l) with rank q Let be the value of b that solves the constrained minimization problem a Show that the Lagrangian for the minimization problem is L(b, ) (Y Xb)(Y Xb) (Rb r), where is ...

a This follows from the definition of the Lagrangian b The first ...

Consider the problem of minimizing the sum of squared residuals subject to the constraint that Rb =

Question:

Consider the problem of minimizing the sum of squared residuals subject to the constraint that Rb = r, where R is q Ã— (k + l) with rank q. Let Î² be the value of b that solves the constrained minimization problem.
a. Show that the Lagrangian for the minimization problem is L(b, Î³) = (Y - Xb)€²(Y - Xb) + Î³€²(Rb - r), where Î³ is a q Ã— 1 vector of Lagrange multipliers.
b. Show that