I would like to find the optimal solution to the optimization problem:
$\min_x x^TMx+c^Tx$
s.t $Ax=b$
where M is PD, A is m over n matrix, M is n over n matrix, x and c are n-dimensional vectors over R and b is m-dimensinal vector over R .
I defined the Lagrangian:
$L(x,\lambda)= x^TMx+c^Tx+ \lambda(Ax-b)$
and then I derivated it:
$\nabla_x L(x,\lambda)= x^T(M+M^T)+c^T+ \lambda A =0$
But I failed to continue, I will highly appriciate some help, thank you.