# Variational calculus - dual problem

#### braindead101

the primal problem was:
min (x^T)Px
i found g(r) and the partial derivative of g(r) w.r.t. x to be: x=-1/2(P^-1)(A^T)r

i have found the dual problem to be:
max -1/4(r^T)A(P^(-1))(A^T)r - (b^T)r
subject to r>= 0
I am told to find x* and r* (which i think is just x and r):
i have not shown my work going from primal to dual as i know it is correct but i have just shown what i think is the necessary information to do this problem.

I am given the following:
A=P=2x2 identity matrix. and b = (1,0)
How do I go about computing x* and r*?
do i just set the max = 0 and calculate r like that, then substitute this r value into the x= formula.
or do i need to partial derivative the dual problem and set to 0 and calculate r like that, then substituting this r value into the x= formula.

please let me know. and am i correct in thinking that x* and r* is the same as x and r...

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