Difference between revisions of "Line search methods"
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=Introduction= | =Introduction= | ||
| − | An algorithm is a line search method if it seeks the minimum of a defined nonlinear function by selecting a reasonable direction vector that, when computed iteratively with a reasonable step size, will provide a function value closer to the absolute minimum of the function. Varying these will change the "tightness" of the optimization. For example, given the function <math>f(x)</math>, an initial <math>x_k</math> is chosen, and the value of <math>f( x_k )</math> is calculated. To find a lower value of <math>f(x)</math>, the value of <math> | + | An algorithm is a line search method if it seeks the minimum of a defined nonlinear function by selecting a reasonable direction vector that, when computed iteratively with a reasonable step size, will provide a function value closer to the absolute minimum of the function. Varying these will change the "tightness" of the optimization. For example, given the function <math>f(x)</math>, an initial <math>x_k</math> is chosen, and the value of <math>f(x_k)</math> is calculated. To find a lower value of <math>f(x)</math>, the value of <math>x_{k+1}</math> is increased |
Revision as of 08:48, 24 May 2015
Author names: Elizabeth Conger
Steward: Dajun Yue and Fengqi You
Contents |
Introduction
An algorithm is a line search method if it seeks the minimum of a defined nonlinear function by selecting a reasonable direction vector that, when computed iteratively with a reasonable step size, will provide a function value closer to the absolute minimum of the function. Varying these will change the "tightness" of the optimization. For example, given the function 
, an initial 
is chosen, and the value of 
is calculated. To find a lower value of , the value of 
is increased
Step Length
Step Direction
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Steepest Descent Method
Newton Method
Quasi-Newton Method
Conclusion
References
1. Sun, W. & Yuan, Y-X. (2006) Optimization Theory and Methods: Nonlinear Programming (Springer US) p 688.
2. Anonymous (2014) Line Search. (Wikipedia). http://en.wikipedia.org/wiki/Line_search.
3. Nocedal, J. & Wright, S. (2006) Numerical Optimization (Springer-Verlag New York, New York) 2 Ed p 664.
