Let $f(X)$ be convex and continuous function , with $X$ a PSD matrix.
Assume that under the affine set of constraints $\mathcal{A}(X)=b$ and the convex constraint $f(X)\le1$ there is an optimal, unique solution $X^*$ for which $f(X^*)$ is maximal.
How can I maximize $f(X)$ under the constraints $\mathcal{A}(X)=b$, $f(X)\le1$ and $X\ge0$?