MosekTools

MosekTools is a Python package providing high-level optimization tools for regression and portfolio optimization problems, built on top of the powerful MOSEK 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

🚀 Quick Start

Installation

pip install mosektools

Important: You need a valid MOSEK license 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

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

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

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

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 for details on:

Setting up the development environment
Running tests and linting
Submitting pull requests
Code style guidelines

To get started with development:

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 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.

🔗 Links

Documentation: https://tschm.github.io/MosekRegression/book
Repository: https://github.com/tschm/MosekRegression
Issues: https://github.com/tschm/MosekRegression/issues
MOSEK: https://www.mosek.com/

🙏 Acknowledgments

Built on the shoulders of MOSEK - a powerful commercial-grade optimization solver for large-scale mathematical optimization problems.

MosekRegression

Install / Use

README