I'm trying to find out what would be the minimum value of the expression below, and at that point, what value does $q(x)$ hold in terms of $p(x)$
The expression is:
$$\displaystyle \int_{-\inf}^{+\inf} (p(x) + q(x))\log\left(\frac{2p(x)}{p(x)+q(x)}\right)dx$$
where $p(x)$ and $q(x)$ are both probability density functions. So their integral from -inf to -inf for x if 1.0 And also, $p(x) \ge 0$ and $q(x) \ge 0$ for all x.