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| 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.
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| ==Motivation==
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| 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.)
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| ==Algorithm==
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| :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> | |
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| :ii) Until <math>\scriptstyle \alpha_j\,</math> satisfies the [[Wolfe conditions|Wolfe condition]]: | |
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| ::<math>\alpha_{j+1}=\tau\alpha_j,\,</math>
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| ::<math> j=j+1.\,</math>
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| :iii) Return <math>\scriptstyle \alpha=\alpha_j.\,</math>
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| In other words, reduce <math>\scriptstyle \alpha^0</math> geometrically, with rate <math>\scriptstyle\tau\,</math>, until the Wolfe condition holds.
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| ==See also== | |
| *[[Line search]]
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| ==References==
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| * {{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}}
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| * {{cite book | first1= J. |last1=Nocedal |first2= S. J.|last2= Wright|title= Numerical optimization|publisher= Springer Verlag|location= New York, NY|year= 1999}}
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| [[Category:Mathematical optimization]]
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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)