Backlash (engineering): Difference between revisions

Revision as of 13:05, 27 January 2014

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, 1^{T} \vec{x} = | \vec{x} |_{1} = 1

where $\vec{x} \in ℝ_{+ +}^{n}$ is the optimization variable, $A \in ℝ^{m \times n}$ and $b \in ℝ^{m}$ are problem parameters, and $1$ denotes a vector whose components are all 1.

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+{{Expert-subject|Mathematics|date=November 2008}}
+An '''[[entropy]] maximization problem''' is a [[convex optimization]] problem of the form
+:maximize <math>f_0(\vec{x}) = - \sum_{i=1}^n x_i \log x_i </math>
+: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}}