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Update algorithm.md - Formatting on Docs
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Aero-Spec authored Sep 22, 2024
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Expand Up @@ -84,13 +84,14 @@ that has been split d times will have a width of $3^−d$. If we have $n$ dimens
r = \sqrt{\left( \frac{1}{2 \cdot 3^{-d_1}} \right)^2 , \ldots , \left( \frac{1}{2 \cdot 3^{-d_n}} \right)^2}
```
---
- Interval splitting in multiple dimensions for DIRECT requires choosing an ordering for the split dimensions
- **Interval splitting in multiple dimensions for DIRECT** requires choosing an ordering for the split dimensions:

![page_16](https://github.com/user-attachments/assets/962993d9-372a-4733-9d1f-0260cdacdff1)
![page_16](https://github.com/user-attachments/assets/962993d9-372a-4733-9d1f-0260cdacdff1)

- DIRECT will only split the longest dimensions of intervals. The algorithm only divides intervals larger than a minimum radius. This minimum radius prevents inefficient function evaluations very close to existing points.
- **DIRECT will only split the longest dimensions of intervals**. The algorithm only divides intervals larger than a minimum radius. This minimum radius prevents inefficient function evaluations very close to existing points:

![page_17](https://github.com/user-attachments/assets/99caea66-02b5-4371-90e2-69305c035ddf)

![page_17](https://github.com/user-attachments/assets/99caea66-02b5-4371-90e2-69305c035ddf)

---
## Practical Implementations:
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