OSQP solver documentation

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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.



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.


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.


It has an easy interface to generate customized embeddable C code with no memory manager required.


It requires no external library to run.

Efficiently warm started

It can be easily warm-started and the matrix factorization can be cached to solve parametrized problems extremely efficiently.


It can be interfaced to C, C++, Fortran (soon!), Python, Julia and Matlab.


OSQP is distributed under the Apache 2.0 License


The following people have been involved in the development of OSQP:

Interfaces development

  • Nick Gould (Rutherford Appleton Laboratory): Fortran and CUTEst interfaces

  • Ed Barnard (University of Oxford): Rust interface

Bug reports and support

Please report any issues via the Github issue tracker. All types of issues are welcome including bug reports, documentation typos, feature requests and so on.

Numerical benchmarks

Numerical benchmarks against other solvers are available here.