Entropy maximization

maximize $f_0(\vec{x}) = - \sum_{i=1}^n x_i \log x_i$
subject to $A\vec{x} \leq b, \quad \mathbf{1}^T \vec{x} = |\vec{x}|_1 =1$
where $\vec{x} \in \mathbb{R}^n_{++}$ is the optimization variable, $A\in\mathbb{R}^{m\times n} \$ and $b \in\mathbb{R}^m \$ are problem parameters, and $\mathbf{1}$ denotes a vector whose components are all 1.