5,321
edits
Numerical Optimization: Difference between revisions
no edit summary
No edit summary |
|||
| Line 2: | Line 2: | ||
==Convergence Rates== | |||
[https://en.wikipedia.org/wiki/Rate_of_convergence Wikipedia]<br> | |||
The rate of convergence is <math>\lim_{k \rightarrow \infty} \frac{|x_{k+1}-x^*|}{|x_{k}-x^*|^q}=L</math><br> | |||
Iterative methods have the following convergence rates: | |||
* If Q=1 and L=1 we have sublinear. | |||
* If Q=1 and <math>L\in(0,1)</math> we have linear convergence. | |||
* If Q=1 and <math>L=0</math> we have superlinear convergence. | |||
* If Q=2 and <math>L \leq \infty</math> we have quadratic convergence. | |||
==Line Search Methods== | ==Line Search Methods== | ||
Basic idea: | Basic idea: | ||