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# Entropy maximization

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 Title: Entropy maximization Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:

### Entropy maximization

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

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.