Entropy maximization

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An entropy maximization problem is a convex optimization problem of the form

maximize $f_0(x) = - \sum_{i=1}^n x_i \log x_i$

subject to $Ax \leq b, \quad \mathbf{1}^T x =1$

where $x \in \mathbb{R}^n_{++}$ 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.