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.