PyNopt (Python Numerical Optimization)

PyNopt is an object-oriented Python library for numerical optimization.

Originally conceived as an evolution of a project for the Numerical Optimization for Large-Scale Problems course at Politecnico di Torino, it has been engineered from the ground up to showcase production-ready software engineering practices combined with rigorous numerical optimization techniques.

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Features

Mathematical Capabilities

• Zero-Order Solvers: Nelder-Mead (Derivative-free optimization)
• First-Order Solvers: Gradient Descent and Projected Gradient Descent.
• Second-Order Solvers: Modified Newton Method.
• Line Search Strategies: Backtracking (Armijo condition), for general-purpose optimization, and Feasible Direction and Projection Arc methods for constrained optimization.
• Constrained Optimization: Built-in support for box constraint, Euclidean ball constraint and active-set handling.
• Computational Tracking: Automatic tracking of function, gradient, and Hessian evaluations (n_feval, n_geval, n_heval) to facilitate empirical complexity analysis.

Software Engineering

• Clean Architecture: Strongly typed (Mypy/typing), utilizing Python Generics (TypeVar) for state management.
• Design Patterns: Heavy use of Strategy (Step Strategies, Convergence Checkers) and Template Method (Objective Functions).
• Fail-Fast API: Input validation blocks mathematical impossibilities before runtime.
• CI/CD Pipeline: Fully automated test suite powered by pytest and GitHub Actions, testing matrix across multiple Python versions.

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Installation

Clone the repository and install it in editable mode using the standard pyproject.toml workflow:

git clone https://github.com/samuuuu0/PyNopt.git
cd PyNopt
pip install -e .

Quick Start

PyNopt's API is designed to be intuitive and modular. Here's how to solve the Rosenbrock function using the Modified Newton solver with Backtracking line search:

import numpy as np
from pynopt import ModifiedNewtonSolver, Rosenbrock

# 1. Initialize the benchmark problem
problem = Rosenbrock()
x0 = np.array([-1.2, 1.0])  # Difficult starting point

# 2. Configure the solver with a Strategy Pattern
solver = ModifiedNewtonSolver(strategy="backtracking", max_iter=100, tol_stat=1e-6)

# 3. Solve the problem and print the optimization result
result = solver.solve(problem, x0)
print(result)

Output

Optimization Result: 
----------------------------------------
  Status:       Success (Stationarity criterion met)
  Iterations:   21
  Optimal f(x): 8.004303e-19
  Optimal x:    [1., 1.]
----------------------------------------
  Function evals: 50
  Gradient evals: 22
  Hessian evals:  21
  Time elapsed:   0.0026 s
----------------------------------------

Plot

The Modified Newton Solver (with Backtracking Line Search) converging to the minimum on the notoriously difficult, non-convex Rosenbrock function.

Analytics & Notebooks

The notebooks/ directory contains analyses and visual benchmarks of the algorithms.

• 01_projected_gradient_analysis.ipynb: Analysis of constrained optimization boundaries.
• 02_nelder_mead_analysis.ipynb: Behavior of zero-order methods.

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Testing

The library includes a test suite ensuring both mathematical accuracy and architectural integrity.

pip install pytest pytest-cov
pytest test/ --cov=pynopt

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Developed by Samuele