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Comparative benchmark of QP solvers

Solvers:

• qpmad -> https://github.com/asherikov/qpmad
• qpOASES -> https://github.com/coin-or/qpOASES
• eiquadprog-fast -> https://github.com/stack-of-tasks/eiquadprog

Results

• All problems are dense and positive-definite.
• qpOASES is used with MPC option preset, this gives ~50% performance boost compared to default preset.
• Time measurements include only the time required to solve a problem; other operations, such as initialization of the solver or reshaping of the constraints, are not taken into account.

oneshot (qpOASES)

• The problem set includes 'standalone' problems distributed with qpOASES -> https://github.com/coin-or/qpOASES/tree/misc/testingdata/cpp/problems, positive-semidefinite problems are skipped.

• Hotstarting is not used.

Time (second) required to solve each of the problems:

The same plot with logarithmic scale:

iterative (qpOASES)

• The problem set includes MPC problems distributed with qpOASES -> https://github.com/coin-or/qpOASES/tree/misc/testingdata/cpp/oqp, all of them have constant Hessian and varying constraints.

• qpOASES is hotstarted starting from the second problem in the sequence, factorization of the Hessian is reused by qpmad in the same way.

• eiQuadProg does not produce the exact answer (up to 1e-9 precision) on some of the problems.

Plots correspond to specific MPC problems and demonstrate time (second) taken by the solvers on each MPC iteration: