Update usage.md - Made Tim's requested changes

docs/src/usage.md

@@ -5,25 +5,24 @@ To use the `DividedRectangles` module, start your code with:
 ```julia
 using DividedRectangles
 ```
-
 ---
 
 ## Core Functions
 
 ### `optimize`
 The `optimize` function is the primary function of the `DividedRectangles` module. It implements the DIRECT algorithm to find the minimum of a given objective function within specified bounds.
 
-To use the `optimize` function with a custom mathematical function:
+To use the `optimize` function with a custom objective function::
 
 ```julia
 using DividedRectangles
 
 # Define the objective function
-f(x) = dot([1.0, 2.0, 3.0], x)  # Example objective function with coefficients
+f(x) = x[1]^2 + x[2]^2 + 3 * sin(5 * x[1]) + 2 * cos(3 * x[2])  # Multivariate example
 
 # Set the search bounds
-a = [0.0, 0.0, 0.0]
-b = [1.0, 1.0, 1.0]
+a = [-2.0, -2.0]
+b = [2.0, 2.0]
 
 # Call the optimization function
 result = optimize(f, a, b)
@@ -42,43 +41,3 @@ println("Best design found: ", result)
 **Returns:** 
 - The best design 𝑥 found by DIRECT.
 ---
-
-### Example: Multivariate Optimization
-
-The following example shows how to optimize a multivariate function using the DIRECT algorithm:
-
-```julia
-using DividedRectangles
-
-# Define the objective function
-f(x) = x[1]^2 + x[2]^2 + 3 * sin(5 * x[1]) + 2 * cos(3 * x[2])
-
-# Set the search bounds
-a = [-2.0, -2.0]
-b = [2.0, 2.0]
-
-# Optimize
-result = DividedRectangles.optimize(f, a, b)
-
-println("Best design found: ", result)
-```
----
-
-### Parameters
-- `f`: This is the objective function to minimize. Should be an operation that accepts a vector of Float64 values.
-- `a`: Vector representing the lower bounds of the search space.
-- `b`: Vector representing the upper bounds of the search space.
-- `max_iterations`:  Maximum number of iterations for the optimization (default: 100).
-- `min_radius`: Minimum size of hyper-rectangles (`default: 1e-5`).
----
-
-## Advanced Usage
-### Fine-Tuning Optimization:
-The `optimize` function offers several parameters for fine-tuning the optimization process:
-
-- `max_iterations`: Sets the maximum number of iterations. Increasing this value can improve accuracy but requires more computational time.
-- `min_radius`: Specifies the minimum size of hyper-rectangles to control the granularity of the search.
-
-```julia
-result = DividedRectangles.optimize(f, a, b, max_iterations=500, min_radius=1e-6)
-```