This repository implements a primal-dual interior-point method to solve quadratic programs of the form

$$ \begin{split} \underset{x}{\text{minimize}} \quad & \frac{1}{2}x^\top Q x + q^\top x \\ \text{subject to} \quad & Gx \preceq h, \\ \quad & Ax = b. \end{split} $$

Example usage is in main.cpp. Implementation follows the outlined algorithm in Section 5 of the CVXGEN paper. The core logic is implemented in solve() function of src/ipm.cpp.

The algorithm includes:

• Prediction (affine), centering, and correcting steps
• Permuted $LDL^\top$ factorization to solve the formulated quasi-definite KKT system, to exploit sparsity
• KKT system regularization, and iterative refinement

Usage follows as

git clone --recurse-submodules [email protected]:as2626/qp_ipm.git \
&& mkdir build

and possibly

cd eigen \
&& mkdir build \
&& cd build \
&& cmake .. \
&& make install

Acknowledgement

N.B., much credit goes to Govind Chari for a reference implementation.