ReHLine-PO

Fast mini-Portfolio Optimization solver fueled by ReHLine. It is particularly good at solving the problems of the kind $$\min_{\mathbf{w} \in \mathbb{R}^n} \frac{C}{2} \mathbf{w}^T G \mathbf{w} - \mu^T \mathbf{w} + \sum_{i=1}^n \phi_i(w_i)$$

where $\phi_i$ are piecewise linear convex cost functions, e.g. it could represent empirical market impact (from the orderbook) + cost from the spread.

Table of contents

• Installation
• Usage
• Benchmarks
• Technical details
• Dependencies
• References

Installation

git clone https://github.com/softmin/ReHLine-PO.git

Usage

# linear constraints Ax + b >= 0
A = np.r_[np.c_[np.ones(n), np.ones(n)*-1.0].T, np.eye(n)]
b = np.r_[-1.0, 1.0, np.zeros(n)]
# other variables (previous weights, transaction costs)
...

from rehline_po import MeanVariance

pf = MeanVariance(mu, cov, A, b, w_prev, transaction_costs)
w = pf.max_quad_util_portf(tol, risk_aversion)

Benchmarks

Benchmark against other convex solvers can be found in benchmarks/.

Technical Details

As the naming suggests, ReHLine-PO is based on an optimization algorithm ReHLine. Mathematical details of the implemetation can be found at

Dependencies

• Python 3.12+
• NumPy 1.26+
• SciPy 1.14+
• PLQ-Composite-Decomposition
• ReHLine-python

References

• [1] Dai, B., & Qiu, Y. (2023, November). ReHLine: Regularized Composite ReLU-ReHU Loss Minimization with Linear Computation and Linear Convergence. In Thirty-seventh Conference on Neural Information Processing Systems.