optimization with ellipsoidal constraints

Question

I'm reading a paper recently and encounter a optimization equation which I can't understand:
$\max_{x\in\{x|x^TPx\le1\}} c^Tx =(cP^{-1}c^T)^{1/2} $ where $P\succ0$

Anybody knows why the result is $(cP^{-1}c^T)^{1/2} $?

Answer 1

From my working here using Langrange multiplier, I have shown that the optimal solution is $$x = \frac{P^{-1}c}{\sqrt{c^TP^{-1}c}}$$

Hence $$c^Tx=\frac{c^TP^{-1}c}{\sqrt{c^TP^{-1}c}}=\sqrt{c^TP^{-1}c}$$