Minimizing a strictly convex quadratic function over 2 norm ball

Question

Let $x, b\in \mathbb{R}^n$ and let $P$ be a $n \times n$ positive definite symmetrix matrix. $r$ is a positive number. What is the minimum of this problem?

$$\begin{array}{ll} \text{minimize} & x^T P x+2 b^Tx\,\\ \text{subject to} & x^T x \leq r\end{array}$$

It seems this problem has an explicit solution, I am surprised that I couldn’t find it on the internet since it is just a special case of the trust region subproblem.

Answer 1

I think I have one answer though. Look at this paper http://users.clas.ufl.edu/hager/papers/Regular/sphere.pdf