Severi–Brauer variety: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
en>John of Reading
m Typo/general fixing, replaced: the the → if the using AWB (8853)
 
cite Jacobson (1996)
 
Line 1: Line 1:
In (unconstrained) [[optimization (mathematics)|optimization]], the '''backtracking linesearch''' strategy is used as part of a [[line search]] method, to compute how far one should move along a given search direction.
I'm Lona and I live in Jaragua Do Sul. <br>I'm interested in Anthropology and Sociology, Gymnastics and Portuguese art. I like to travel and watching Modern Family.<br><br>Here is my web page; http://www.hostgator1centcoupon.info/ ([http://www.paugercarbon.com/?option=com_k2&view=itemlist&task=user&id=61143 www.paugercarbon.com])
 
==Motivation==
 
Usually it is undesirable to exactly minimize the function <math>\displaystyle \phi(\alpha)</math> in the generic linesearch algorithm. One way to inexactly minimize <math>\displaystyle \phi</math> is by finding an <math>\displaystyle \alpha_k</math> that gives a sufficient decrease in the [[objective function]] <math>f:\mathbb R^n\to\mathbb R</math> (assumed [[smooth function|smooth]]), in the sense of the [[Wolfe conditions|Wolfe condition]] holding. This condition, when used appropriately as part of a backtracking linesearch, is enough to generate an acceptable step length. (It is not sufficient on its own to ensure that a reasonable value is generated, since all <math>\displaystyle \alpha</math> small enough will satisfy the Wolfe condition. To avoid the selection of steps that are too short, the additional [[Wolfe conditions|curvature condition]] is usually imposed.)
 
==Algorithm==
 
:i) Set iteration counter <math>\scriptstyle j\,=\,0</math>. Make an initial guess <math>\scriptstyle \alpha^0\,>\,0</math> and choose some <math>\scriptstyle \tau\,\in\,(0,1).\,</math>
 
:ii) Until <math>\scriptstyle \alpha_j\,</math> satisfies the [[Wolfe conditions|Wolfe condition]]:
 
::<math>\alpha_{j+1}=\tau\alpha_j,\,</math>
 
::<math> j=j+1.\,</math>
 
:iii) Return <math>\scriptstyle \alpha=\alpha_j.\,</math>
 
In other words, reduce <math>\scriptstyle \alpha^0</math> geometrically, with rate <math>\scriptstyle\tau\,</math>, until the Wolfe condition holds.
 
==See also==
*[[Line search]]
 
==References==
* {{cite book | first1= J. E. |last1= Dennis |first2= R. B.|last2= Schnabel|title= Numerical Methods for Unconstrained Optimization and Nonlinear Equations|publisher=SIAM Publications|location= Philadelphia|year= 1996}}
* {{cite book | first1= J. |last1=Nocedal |first2= S. J.|last2= Wright|title= Numerical optimization|publisher= Springer Verlag|location= New York, NY|year= 1999}}
 
[[Category:Mathematical optimization]]

Latest revision as of 17:17, 5 May 2014

I'm Lona and I live in Jaragua Do Sul.
I'm interested in Anthropology and Sociology, Gymnastics and Portuguese art. I like to travel and watching Modern Family.

Here is my web page; http://www.hostgator1centcoupon.info/ (www.paugercarbon.com)