:) 
The question I am working on is as follows:

Given an $n$ dimensional vector $R \in \mathcal{R}^n$, and a convex set $G=\{\mu \in \mathcal{R}^n | \mu_i \ge 0, ~ \mu^T \mathbf{1}=1, ~ A\mu =0 \}$ where $\mathbf{1}= [1, 1, ..., 1]^T$. ($A \in \mathcal{R}^{m \times n}$ and $m < n$) We assume that the set $G$ is not an empty set. 

Suppose $\bar{\mu} = \arg \max_{\mu \in G} R^T\mu$ given $R$. 
Then can we say $\tilde{\mu} = \arg \max_{\mu \in G} \bar{\mu}^T\mu$ is identical to $\bar{\mu}$? 

I believe this problems is closely related to the relationship between reinforcement learning and inverse reinforcement learning.