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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...