Any clues about how to prove that the following function is strongly-concave in $x$? (We conjecture it is $2$-strongly concave but cannot prove it. We have already proved strict concavity through using the fact that $x^2$ is operator (strictly) concave). $$ f(x): S^n \rightarrow R, \ x \mapsto {\rm tr}\left(\sqrt{{\rm Diag}(x) - x x^T}\right), $$ where $x$ is a column vector in the unit simplex. i.e., $x \geq 0$, $\sum_jx_j = 1$, $\sqrt{}$ is the matrix square root function, and ${\rm Diag(x)}$ is a diagonal matrix which stores entries of $x$ on its diagonal.
Thanks in advance.
