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Numerical Optimization: Difference between revisions
→Convergence Rates
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The rate of convergence is <math>\lim_{k \rightarrow \infty} \frac{|x_{k+1}-x^*|}{|x_{k}-x^*|^q}=L</math><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: | Iterative methods have the following convergence rates: | ||
* If Q=1 and L=1 we have sublinear. | * If Q=1 and L=1 we have sublinear convergence. | ||
* If Q=1 and <math>L\in(0,1)</math> we have linear convergence. | * 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=1 and <math>L=0</math> we have superlinear convergence. | ||
* If Q=2 and <math>L \leq \infty</math> we have quadratic convergence. | * If Q=2 and <math>L \leq \infty</math> we have quadratic convergence. | ||
==Line Search Methods== | ==Line Search Methods== | ||
Basic idea: | Basic idea: | ||