Update theory.md

docs/src/theory.md

@@ -1,6 +1,6 @@
 # Theory
 
-The DIRECT (DIvided RECTangles) algorithm is a global optimization method that does not require a known Lipschitz constant. This characteristic makes it particularly robust and versatile, applicable to a wide range of optimization problems. The algorithm operates by dividing the search space into smaller hyper-rectangles and evaluating the function at the center of each rectangle.
+The DIRECT (Divided Rectangles) algorithm is a global optimization method that does not require a known Lipschitz constant. This characteristic makes it particularly robust and versatile, applicable to a wide range of optimization problems. The algorithm operates by dividing the search space into smaller hyper-rectangles and evaluating the function at the center of each rectangle.
 
 ---
 ### Key Concepts of the DIRECT Algorithm
@@ -32,17 +32,19 @@ The objective function $f(x)$ is evaluated at the center of each hyper-rectangle
 f(x) = \sum_{i=1}^{n} c_i x_i
 ```
 
-where ($x_i$) are the variables, and ($c_i$) are the corresponding coefficients.
+where $x_i$ are the variables, and $c_i$ are the corresponding coefficients.
 
 - **Rectangle Selection Criterion**:
-  A rectangle ($R$) is considered potentially optimal if:
+  A rectangle $R$ is considered potentially optimal if:
+
 ```math
   f(x_R) - L \cdot r_R \leq f(x) - L \cdot r_x \quad \text{for all } x \in R
 ```
+
   where:
   - $f(x_R)$ is the function value at the center of the rectangle.
-  - ($r_R$) is the radius of the rectangle.
-  -  ($L$) is the Lipschitz constant.
+  - $r_R$ is the radius of the rectangle.
+  - $L$ is the Lipschitz constant.
 
 **Recursive Division**:  
 The hyper-rectangles are recursively divided along their longest dimension:
@@ -51,7 +53,7 @@ The hyper-rectangles are recursively divided along their longest dimension:
 x_R = \frac{a_i + b_i}{2}
 ```
 
-where ($a_i$) and ($b_i$) are the bounds of the rectangle along the ($i$)-th dimension.
+where $a_i$ and $b_i$ are the bounds of the rectangle along the $i$-th dimension.
 
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