# 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 | + | 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. To find a lower value of <math>f(x)</math>, the value of <math>x_{k+1}</math> is increased by the following iteration scheme |

+ | [[File:CodeCogsEqn.gif]] | ||

=Step Length= | =Step Length= |

## Revision as of 10:38, 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. To find a lower value of , the value of is increased by the following iteration scheme

# Step Length

# Step Direction

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Youtube Site

## 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.