# Optimization

- 2 mins

Life is NP hard.

## Rate of Convergence

We say ${x_{k}}$ converges to $x^{\ast}$ if and only if

$$\lim_{k \rightarrow \infty} {\parallel x_{k} - x^{\ast} \parallel}= 0$$

### Converge Sublinearly

$$\lim_{k \rightarrow \infty} \frac{\parallel x_{k+1} - x^{\ast} \parallel}{\parallel x_{k} - x^{\ast} \parallel} = a$$

and $a \in (0,1)$ then the ${x_{k}}$ is said to converge sublinearly.