Entropy maximization

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

maximize ${\displaystyle f_0(\overrightarrow{x})=-{\displaystyle \sum _{i=1}^n}{x}_i\log x_i}$

subject to ${\displaystyle A\overrightarrow{x}\le b,{\displaystyle \sum _{i=1}^n}{x}_i=1}$

where ${\displaystyle \overrightarrow{x}\in {\mathbb{ℝ}}_{++}^n}$ is the optimization variable, ${\displaystyle A\in {\mathbb{ℝ}}^{m\times n}}$ and ${\displaystyle b\in {\mathbb{ℝ}}^m}$ are problem parameters.

• Principle of maximum entropy

• Boyd, Stephen; Lieven Vandenberghe (2004). Convex Optimization. Cambridge University Press. pp. 362. ISBN 0-521-83378-7. https://web.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf#page=376. Retrieved 2008-08-24. 

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