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| In [[Optimization (mathematics)|optimization]], a '''self-concordant function''' is a [[function (mathematics)|function]] <math>f:\mathbb{R} \rightarrow \mathbb{R}</math> for which
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| : <math>|f'''(x)| \leq 2 f''(x)^{3/2}.</math>
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| A function <math>g(x) : \mathbb{R}^n \rightarrow \mathbb{R}</math> is self-concordant if its restriction to any arbitrary line is self-concordant.
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| == Properties ==
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| Self concordance is preserved under addition, [[affine transformation]]s, and scalar multiplication by a value greater than one.
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| == Applications ==
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| Among other things, self-concordant functions are useful in the analysis of [[Newton's method]]. Self-concordant ''barrier functions'' are used to develop the [[barrier function]]s used in [[interior point method]]s for convex and nonlinear optimization.
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| == References ==
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| {{Reflist}}
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| * {{cite book
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| |title=Convex Optimization
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| |last1= Boyd|first1=Stephen P.|authorlink1=
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| |first2=Lieven |last2=Vandenberghe
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| |editor1-last= |editor1-first= | editor1-link=
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| |year=2004
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| |publisher=Cambridge University Press
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| |location=
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| |isbn=978-0-521-83378-3
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| |pages=
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| |url=http://www.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf
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| |format=pdf
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| |accessdate=October 15, 2011}}
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| {{mathapplied-stub}}
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| [[Category:Mathematical optimization]]
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Latest revision as of 20:20, 21 September 2014
Hi there! :) My name is Rosario, I'm a student studying Greek and Roman Culture from Rio De Janeiro, Brazil.
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