Entropy maximization

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

maximize ${\displaystyle f_{0}({\vec {x}})=-\sum _{i=1}^{n}x_{i}\log x_{i}}$

subject to ${\displaystyle A{\vec {x}}\leq b,\quad \sum _{i=1}^{n}x_{i}=1}$

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

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.