Entropy maximization

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

minimize $f_{0}(x)=\sum _{i=1}^{n}x_{i}\log x_{i}$

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\ n\mathbb {R} ^{m}\$ are problem parameters, and $\mathbf {1}$ denotes a vector whose components are all 1.