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{{Expert-subject|Mathematics|date=November 2008}}
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An '''[[entropy]] maximization problem''' is a [[convex optimization]] problem of the form
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:maximize <math>f_0(\vec{x}) = - \sum_{i=1}^n x_i \log x_i </math>
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:subject to <math>A\vec{x} \leq b, \quad \mathbf{1}^T \vec{x}  = |\vec{x}|_1 =1</math>
 
where <math>\vec{x} \in \mathbb{R}^n_{++}</math> is the optimization variable, <math>A\in\mathbb{R}^{m\times n} \ </math> and <math> b \in\mathbb{R}^m \ </math> are problem parameters, and <math>\mathbf{1}</math> denotes a vector whose components are all 1.
 
==See also==
* [[Principle of maximum entropy]]
 
==External links==
* {{cite book
        |last=Boyd
        |first=Stephen
        |coauthors=Lieven Vandenberghe
        |title=Convex Optimization
        |publisher=[[Cambridge University Press]]
        |date=2004
        |pages=p. 362
        |isbn=0-521-83378-7
        |url=http://www.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf
        |accessdate=2008-08-24
}}
 
[[Category:Mathematical optimization]]
[[Category:Convex optimization]]
 
{{mathapplied-stub}}

Latest revision as of 00:20, 11 December 2014

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