Non Linear optimization of non central parameter

Question

optimize for $p_{i}$, $i$ = 1,2,3.

$(\frac{p_{3}}{1-p_3}(\mu_3 - \sum_{i=1}^{3}p_{i}\mu_i)^2)$

given that $\sum_{i=1}^{3}p_{i}\mu_{i}-\mu_3\leq 0$ and $\sum_{i=1}^{3}p_{i} = 1$. $0\leq p_i\leq 1$ for $i = 1,2,3.$

KKT may help