This repository implements a simple QP solver using an Augmented Lagrangian method. Specifically, problems of the following form are handled (with JIT support):

$$\min\limits_{x} 0.5 x^T P x + q^T x \qquad \mbox{s.t.} \quad Cx = d \wedge Gx <= h$$

We also support problems of the following form:

$$\min\limits_{x} 0.5 x^T P x + q^T x \qquad \mbox{s.t.} \quad l <= Ax <= u$$

In both cases, we require that $P$ be symmetric positive semi-definite, and that $P + \rho C^T C$ be positive definite for any $\rho &gt; 0$. We should eventually support only requiring $P$ to be symmetric positive semi-definite, by adding a small amount of regularization (similarly to what OSQP does).

My motivation for writing this simple solver is that OSQP often struggles to solve problems to high accuracy in a reasonable number of iterations. It would be interesting to benchmark this simple solver against PIQP, and possibly implementing the latter in JAX. My expectation is that IPM solvers such as PIQP would perform better in the worst case and be more robust, but perhaps take more iterations on easier problems.