Add Momentum SGD optimizer implementation

[Adhithya-Laxman]

Description

This PR implements the Momentum SGD optimizer using pure NumPy as part of the effort to add neural_network/optimizers to the repository.

This PR addresses part of issue #13662 .

What does this PR do?

• Implements Momentum SGD optimizer that accelerates gradient descent by adding momentum to weight updates
• Uses velocity accumulation to dampen oscillations and speed up convergence
• Provides a clean, educational implementation without external deep learning frameworks

Implementation Details

• Algorithm: SGD with momentum
• Update rule:

  velocity = momentum * velocity - learning_rate * gradient
  param = param + velocity
  

• Pure NumPy: No PyTorch, TensorFlow, or other frameworks required
• Educational focus: Clear variable names, detailed docstrings, and comments

Features

✅ Complete docstrings with parameter descriptions
✅ Type hints for all function parameters and return values
✅ Doctests for correctness validation
✅ Usage example demonstrating optimizer on quadratic function
✅ PEP8 compliant code formatting
✅ Momentum accumulation with configurable momentum factor

Testing

All doctests pass:

python -m doctest neural_network/optimizers/momentum_sgd.py -v

Linting passes:

ruff check neural_network/optimizers/momentum_sgd.py

Example output demonstrates proper convergence behavior.

This PR is the second optimizer in the planned sequence outlined in #13662:

• ✅ Stochastic Gradient Descent (SGD) - feat: add SGD optimizer for neural networks #13671
• ✅ Momentum SGD (this PR)
• ⏳ Nesterov Accelerated Gradient (NAG) - upcoming
• ⏳ Adagrad - upcoming
• ⏳ Adam - upcoming
• ⏳ Muon - upcoming

References

• Momentum SGD - Wikipedia
• CS231n: Neural Networks 3

Checklist

• I have read CONTRIBUTING.md
• This pull request is all my own work -- I have not plagiarized
• I know that pull requests will not be merged if they fail the automated tests
• This PR only changes one algorithm file
• All new Python files are placed inside an existing directory
• All filenames are in all lowercase characters with no spaces or dashes
• All functions and variable names follow Python naming conventions
• All function parameters and return values are annotated with Python type hints
• All functions have doctests that pass the automated testing
• All new algorithms include at least one URL that points to Wikipedia or another similar explanation
• [x]

Next Steps

Additional optimizers (Adam, Adagrad, NAG, Muon) will be submitted in follow-up PRs to maintain focused, reviewable contributions.