[Term Entry] Python:SciPy scipy.optimize: minimize() (#5908)

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Co-authored-by: Mamta Wardhani <[email protected]>

* Update content/scipy/concepts/scipy-optimize/terms/minimize/minimize.md

Co-authored-by: Mamta Wardhani <[email protected]>

* Update content/scipy/concepts/scipy-optimize/terms/minimize/minimize.md

Co-authored-by: Mamta Wardhani <[email protected]>

* Update content/scipy/concepts/scipy-optimize/terms/minimize/minimize.md

Co-authored-by: Mamta Wardhani <[email protected]>

* Update content/scipy/concepts/scipy-optimize/terms/minimize/minimize.md

Co-authored-by: Mamta Wardhani <[email protected]>

* Update content/scipy/concepts/scipy-optimize/terms/minimize/minimize.md

Co-authored-by: Mamta Wardhani <[email protected]>

* Modify the last version of minimize term

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* Update minimize.md

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Author: BoLiuV5

content/scipy/concepts/scipy-optimize/terms/minimize/minimize.md

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+---
+Title: 'minimize()'
+Description: 'Returns the minimum of a scalar function of one or more variables using optimization methods from SciPy.'
+Subjects:
+  - 'Data Science'
+  - 'Machine Learning'
+Tags:
+  - 'Math'
+  - 'Optimization'
+  - 'Python'
+
+CatalogContent:
+  - 'learn-python'
+  - 'paths/data-science'
+---
+
+The **`minimize()`** function in the SciPy library is used to find the minimum of a scalar function. It provides various optimization algorithms, including both gradient-based and derivative-free methods.
+
+## Syntax
+
+```python
+scipy.optimize.minimize(fun, x0, args=(), method=None, jac=None, hess=None, constraints=(), bounds=None, tol=None, options=None)
+```
+
+## Parameters
+
+- `fun`: The objective function to be minimized.
+- `x0`: Initial guess for the variables.
+- `args`: Extra arguments passed to the objective function.
+- `method`: The optimization method to use (e.g., `'BFGS'`, `'Nelder-Mead'`, `'Powell'`, etc.).
+- `jac` (Optional): The gradient (Jacobian) of the objective function. If not provided, numerical differentiation is used.
+- `hess` (Optional): The Hessian matrix of the objective function. Typically used with second-order methods like 'Newton-CG' or 'trust-ncg'.
+- `constraints` (Optional): Constraints definition. Can include equality or inequality constraints.
+- `bounds` (Optional): Bounds on variables.
+- `tol` (Optional): Tolerance for termination. Specifies the convergence threshold.
+- `options` (Optional): A dictionary of additional options specific to the selected optimization method (e.g., maximum number of iterations, tolerance, etc.).
+
+It returns an `OptimizeResult` object with the optimal solution, function value at the solution, success status, and other optimization details.
+
+## Example
+
+In this example, we are using the `minimize()` function to find the minimum value of a quadratic objective function:
+
+```py
+from scipy.optimize import minimize
+
+# Define the objective function
+def objective_function(x):
+    return x**2
+
+# Initial guess
+x0 = 2
+
+# Perform the minimization
+result = minimize(objective_function, x0)
+
+# Print the result
+print("Optimal value:", result.fun)
+print("Optimal point:", result.x)
+```
+
+It produces the following output:
+
+```shell
+Optimal value: 3.5662963072207506e-16
+Optimal point: [-1.88846401e-08]
+```
+
+## Codebyte Example
+
+Run the following codebyte example to understand how the `minimize()` function works:
+
+```codebyte/python
+from scipy.optimize import minimize
+
+# Define the objective function
+def objective_function(x):
+    return (x - 3)**2 + 4
+
+# Initial guess
+x0 = 0
+
+# Perform the minimization
+result = minimize(objective_function, x0)
+
+# Print the result
+print("Optimal value:", result.fun)
+print("Optimal point:", result.x)
+```