OSQP solver documentation¶

The OSQP (Operator Splitting Quadratic Program) solver is a numerical optimization package for solving convex quadratic programs in the form

$\begin{split}\begin{array}{ll} \mbox{minimize} & \frac{1}{2} x^T P x + q^T x \\ \mbox{subject to} & l \leq A x \leq u \end{array}\end{split}$

where $$x$$ is the optimization variable and $$P \in \mathbf{S}^{n}_{+}$$ a positive semidefinite matrix.

Code available on GitHub.

Citing OSQP

If you are using OSQP for your work, we encourage you to

We are looking forward to hearing your success stories with OSQP! Please share them with us.

Features

Efficient
It uses a custom ADMM-based first-order method requiring only a single matrix factorization in the setup phase. All the other operations are extremely cheap. It also implements custom sparse linear algebra routines exploiting structures in the problem data.
Robust
The algorithm is absolutely division free after the setup and it requires no assumptions on problem data (the problem only needs to be convex). It just works!
Detects primal / dual infeasible problems
When the problem is primal or dual infeasible, OSQP detects it. It is the first available QP solver based on first-order methods able to do so.
Embeddable
It has an easy interface to generate customized embeddable C code with no memory manager required.
Library-free
It requires no external library to run. Only the setup phase requires the AMD and SparseLDL from Timothy A. Davis that are already included in the sources.
Efficiently warm started
It can be easily warm-started and the matrix factorization can be cached to solve parametrized problems extremely efficiently.
Interfaces
It can be interfaced to C, C++, Python and Matlab.