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MosekRegression
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# MosekTools [](https://raw.githubusercontent.com/tschm/MosekRegression/main/LICENSE) [](https://github.com/tschm/MosekRegression/actions/workflows/rhiza_ci.yml) [](https://www.codefactor.io/repository/github/tschm/MosekRegression) **MosekTools** is a Python package providing high-level optimization tools for regression and portfolio optimization problems, built on top of the powerful [MOSEK](https://www.mosek.com/) optimization solver. ## 🎯 Features - **Regression Methods** - Least Squares (unconstrained and positivity-constrained) - LASSO Regression (L1-regularized) - L1-penalized Least Squares - **Portfolio Optimization** - Markowitz Mean-Variance Optimization - Minimum Variance Portfolio - Risk-Objective Portfolio Optimization - **Built on MOSEK Fusion API** - Efficient conic optimization - Production-grade solver performance - Support for large-scale problems ## 📚 Documentation Full documentation and interactive examples are available at [https://tschm.github.io/MosekRegression/book](https://tschm.github.io/MosekRegression/book) ## 🚀 Quick Start ### Installation ```bash pip install mosektools ``` **Important**: You need a valid [MOSEK license](https://www.mosek.com/products/academic-licenses/) to use this package. Academic licenses are available free of charge. **Note**: The package is installed as `mosektools` (no underscore), but imported as `mosek_tools` (with underscore). ### Basic Usage #### Least Squares Regression ```python import numpy as np from mosek_tools.solver import lsq_ls # Generate sample data A = np.random.randn(100, 10) b = np.random.randn(100) # Solve unconstrained least squares: min ||Ax - b||_2^2 # Mosek License needed here: # x = lsq_ls(A, b) ``` #### LASSO Regression ```python from mosek_tools.solver import lasso # Solve LASSO: min ||Ax - b||_2^2 + lambda * ||x||_1 lambda_param = 0.1 # Mosek License needed here: # x = lasso(A, b, lambda_param) ``` #### Portfolio Optimization ```python from mosek_tools.solver import markowitz import numpy as np # Expected returns and covariance matrix expected_returns = np.array([0.12, 0.10, 0.07, 0.03]) covariance = np.array([ [0.04, 0.01, 0.00, 0.00], [0.01, 0.02, 0.00, 0.00], [0.00, 0.00, 0.01, 0.00], [0.00, 0.00, 0.00, 0.005] ]) # Solve Markowitz problem with risk aversion parameter risk_aversion = 2.0 # Mosek License needed here: # weights = markowitz(expected_returns, covariance, risk_aversion) ``` ## 📖 API Reference ### Regression Functions - `lsq_ls(matrix, rhs)` - Unconstrained least squares - `lsq_pos(matrix, rhs)` - Least squares with positivity constraints - `lsq_pos_l1_penalty(matrix, rhs, gamma, lamb)` - L1-penalized least squares - `lasso(matrix, rhs, lamb)` - LASSO regression ### Portfolio Optimization Functions - `markowitz(exp_ret, covariance_mat, aversion)` - Mean-variance optimization - `markowitz_riskobjective(exp_ret, covariance_mat, bound)` - Risk-objective formulation ### Utility Functions - `create_model()` - Create a MOSEK optimization model context manager ## 🔧 Requirements - Python >= 3.11 - NumPy >= 2.3.4 - MOSEK >= 11.0.29 (with valid license) ## 💡 Motivation This package was created to support the experiments described in the paper: > **"A Least Squares Approach to Direct Data-Driven Control"** > Schmelzer, Hauser, Dahl, and Andersen > [arXiv:1310.3397](http://arxiv.org/abs/1310.3397) The tools have since been extended to support a broader range of optimization problems in regression and portfolio management. ## 🤝 Contributing Contributions are welcome! Please see our [Contributing Guide](CONTRIBUTING.md) for details on: - Setting up the development environment - Running tests and linting - Submitting pull requests - Code style guidelines To get started with development: ```bash git clone https://github.com/tschm/MosekRegression.git cd MosekRegression make install make test ``` ## 📄 License This project is licensed under the MIT License - see the [LICENSE](LICENSE) file for details. **Note**: While this package is MIT licensed, MOSEK itself requires a separate license. Academic licenses are available free of charge from [MOSEK](https://www.mosek.com/products/academic-licenses/). ## 🔗 Links - **Documentation**: [https://tschm.github.io/MosekRegression/book](https://tschm.github.io/MosekRegression/book) - **Repository**: [https://github.com/tschm/MosekRegression](https://github.com/tschm/MosekRegression) - **Issues**: [https://github.com/tschm/MosekRegression/issues](https://github.com/tschm/MosekRegression/issues) - **MOSEK**: [https://www.mosek.com/](https://www.mosek.com/) ## 🙏 Acknowledgments Built on the shoulders of [MOSEK](https://www.mosek.com/) - a powerful commercial-grade optimization solver for large-scale mathematical optimization problems.
