# OSQP solver documentation¶

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questions related to the solver!**

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

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.

- 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++, Fortran (soon!), Python, Julia and Matlab.

License

OSQP is distributed under the Apache 2.0 License

Credits

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

Bartolomeo Stellato (Princeton University): main development

Goran Banjac (ETH Zürich): main development

Nicholas Moehle (Stanford University): methods, maths, and code generation

Paul Goulart (University of Oxford): methods, maths, and Matlab interface

Alberto Bemporad (IMT Lucca): methods and maths

Stephen Boyd (Stanford University): methods and maths

Ian McInerney (Imperial College London): software engineering, code generation

Vineet Bansal (CSML, Princeton University): software engineering

Michel Schubiger (Schindler R&D): GPU implementation

John Lygeros (ETH Zurich): methods and maths

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.