OSQP solver documentation

Visit our GitHub Discussions page for any 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

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

where \(x \in \mathbf{R}^n\) 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

• Cite the related papers

• Put a star on GitHub

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 provides interfaces to C, C++, Fortran, Julia, Matlab, Python, R, Ruby, and Rust.

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 (Princeton University): software engineering

• Michel Schubiger (Schindler R&D): GPU implementation

• John Lygeros (ETH Zurich): methods and maths

• Amit Solomon (Princeton University): software engineering

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.