optimization-library 1.0.4

A Python library for linear, nonlinear, and integer programming

Optimization Library

A Python library for solving linear, nonlinear, and integer programming problems. The library provides a collection of optimization algorithms for tasks such as the diet problem, model parameter optimization, and the 0-1 knapsack problem.

Features

• Linear Programming: Solve problems like the diet problem using methods such as Simplex, Relaxation, Column Generation, ADMM, and Mirror Descent.
• Nonlinear Programming: Optimize model parameters with methods like Gradient Descent, Newton's Method, Steepest Descent, Adam, and Nelder-Mead.
• Integer Programming: Solve the 0-1 knapsack problem using Branch and Bound, Gomory Cuts, Cutting Planes, Lagrangian Relaxation, and Sherali-Adams (Level 1).
• Visualization and logging of optimization results using Matplotlib and Pandas.

Installation

Install the library using pip:

pip install optimization-library

Requirements

• numpy~=2.3.0
• cvxpy~=1.6.5
• pandas~=2.3.0
• matplotlib~=3.10.3
• PuLP~=3.2.1
• scipy~=1.15.3
• openpyxl~=3.1.5

Usage

Linear Programming

import numpy as np
from optimization_library import solve_lp, post_processing_linear_approximation_logs

c = np.array([3, 2], dtype=float)
A = np.array([[1, 1], [2, 1]], dtype=float)
b = np.array([4, 5], dtype=float)
methods = ["simplex", "ADMM"]

results = [solve_lp(method, c, A, b, epsi=1e-6, is_maximization=True) for method in methods]
post_processing_linear_approximation_logs(results, visual=True, file_print=True)

Nonlinear Programming

import numpy as np
from optimization_library import solve_nlp, post_processing_non_linear_approximation_logs

t = np.linspace(0, 2 * np.pi, 10)
y = np.exp(-0.5 * t) + np.sin(-1.2 * t)
model = lambda x, t: np.exp(-x[0] * t) + np.sin(x[1] * t)
x0 = [0.25, 0.25]
bounds = [(-3.5, 2.5), (-4.2, 2.8)]
methods = ["adam", "nelder-mead"]

results = [solve_nlp(method, x0, t, y, model=model, bounds=bounds, epsilon=1e-6) for method in methods]
post_processing_non_linear_approximation_logs(results, visual=True, file_print=True)

Integer Programming

from optimization_library import solve_ip, post_processing_integer_approximation_logs

weights = [2, 3, 4, 5]
values = [3, 4, 5, 6]
capacity = 10
methods = ["branch_and_bound", "gomory"]

results = [solve_ip(method, weights, values, capacity, epsilon=1e-4) for method in methods]
post_processing_integer_approximation_logs(results, visual=True, file_print=True)

Examples

A console application demonstrating the usage of the library is available in the GitHub repository under the examples/ directory. Run it with:

git clone https://github.com/UWFms/optimization-library.git
cd optimization-library
python -m venv venv
venv\Scripts\activate
pip install -r requirements.txt
python example\main.py

License

This project is licensed under the MIT License. See the LICENSE file for details.

Contributing

Contributions are welcome! Please submit issues or pull requests to the GitHub repository https://github.com/UWFms/optimization-library.

Documentation

Full documentation is available at https://disk.yandex.ru/i/k7wqcUCCx1Ym9Q.