Entropy maximization

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

maximize [math]\displaystyle{ f_0(\vec{x}) = - \sum_{i=1}^n x_i \log x_i }[/math]

subject to [math]\displaystyle{ A\vec{x} \leq b, \quad \sum_{i=1}^n x_i = 1 }[/math]

where [math]\displaystyle{ \vec{x} \in \mathbb{R}^n_{++} }[/math] is the optimization variable, [math]\displaystyle{ A\in\mathbb{R}^{m\times n} }[/math] and [math]\displaystyle{ b \in\mathbb{R}^m }[/math] are problem parameters.

See also

• Principle of maximum entropy

External links

• 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.