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We present a general-purpose solver for convex quadratic programs based onthe alternating direction method of multipliers, employing a novel operatorsplitting technique that requires the solution of a quasi-definite linearsystem with the same coefficient matrix at almost every iteration. Ouralgorithm is very robust, placing no requirements on the problem data such aspositive definiteness of the objective function or linear independence of theconstraint functions. It can be configured to be division-free once an initialmatrix factorization is carried out, making it suitable for real-timeapplications in embedded systems. In addition, our technique is the firstoperator splitting method for quadratic programs able to reliably detect primaland dual infeasible problems from the algorithm iterates. The method alsosupports factorization caching and warm starting, making it particularlyefficient when solving parametrized problems arising in finance, control, andmachine learning. Our open-source C implementation OSQP has a small footprint,is library-free, and has been extensively tested on many problem instances froma wide variety of application areas. It is typically ten times faster thancompeting interior-point methods, and sometimes much more when factorizationcaching or warm start is used. OSQP has already shown a large impact with tensof thousands of users both in academia and in large corporations.

OSQP: An Operator Splitting Solver for Quadratic Programs