Self-concordant function: Difference between revisions

Revision as of 20:36, 13 April 2017

Revision as of 20:51, 13 April 2017

Line 11:

and which satisfies <math>f'''(x) = 0</math> elsewhere.

AMore generally, a multivariate function <math>gf(x) : \mathbb{R}^n \rightarrow \mathbb{R}</math> is self-concordant if its restriction to any arbitrary line is self-concordant. <ref>{{cite book

: <math>\left. \frac{d}{d\alpha} \nabla^2 f(x + \alpha y) \right|_{\alpha = 0} \preceq 2 \sqrt{y^T \nabla^2 f(x)\,y} \, \nabla^2 f(x)</math>

or, equivalently, if its restriction to any arbitrary line is self-concordant. <ref>{{cite book

|title=Convex Optimization |last1= Boyd|first1=Stephen P.|authorlink1= |first2=Lieven |last2=Vandenberghe |editor1-last= |editor1-first= | editor1-link= |year=2004 |publisher=Cambridge University Press |___location= |isbn=978-0-521-83378-3 |pages= |url=http://www.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf |format=pdf |accessdate=October 15, 2011}}</ref>