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.

See also

• Principle of maximum entropy

External links

• Boyd, Stephen; Lieven Vandenberghe (2004). Convex Optimization (PDF). Cambridge University Press. p. 362. ISBN 0-521-83378-7. Retrieved 2008-08-24.