SparseRunner

OSQP is fast, but is only for QP, not LP.

The "benchmarks" (https://github.com/osqp/osqp_benchmarks) include some important problem classes but are random so, for general QP, are not valid. On the industry standard benchmarks (http://plato.asu.edu/ftp/qpbench.html) OSQP doesn't look so good, and it's not even tested against commercial solvers (http://plato.asu.edu/ftp/cconvex.html).

Our experience with it on general benchmarking problems is that it can struggle to get sufficiently accurate dual values to the extent that it fails to solve them.

For certain classes of important QP problems, and when optimization to small tolerances is not required, it's undoubtedly a great solver - but it's not a general solver.

For interior point the key is writing a multicore matrix decomposition code that exploits sparsity and the range of problem structure that is encountered. For MIP it's having techniques to exploit the many different problem features that occur and ensuring that they are used intelligently.

Thanks - from HiGHS

Throwing money and people at solver projects is not the way to succeed. Get and keep the right 1-2 people, and HiGHS has already shown what is possible.

Thanks. Matching Gurobi is not feasible, but HiGHS wants those who depend on open-source solvers to be able to work with bigger models than is currently possible. Once HiGHS has a good interior point solver (for QP) - the main aim of this proposal - the vision is to develop a nonlinear programming solver.

HiGHS for MIP is meaningfully faster than than SCIP after 18 months, and will get a lot better. SCIP's native LP solver is just simplex (and slower than HiGHS). For these problems you need interior point, and HiGHS is much the best open-source interior point solver for them.

The HiGHS open-source MIP solver is vastly better than Cbc now - and getting better rapidly - although we've got a way to go to be competitive with the best commercial solvers.

For open-source, the HiGHS MIP solver vastly out-performs Cbc now, and is easily called from JuMP

HiGHS is now the default open-source LP/MIP solver in JuMP documentation. Performance-wise, for MIP HiGHS is way ahead of Cbc

Do consider HiGHS. MIP performance is way ahead of Cbc now. For LP, our simplex solver is comparable with Clp, and our interior point solver is well ahead of any open-source solver.

The latest results show HiGHS to be significantly better than vanilla SCIP. If "OSS" means "Open Source Solvers" then COPT isn't open-source and SCIP isn't open source for commercial purposes. Hence the warning given by OR-Tools. HiGHS is very much the best bet going forward for open-source MIP

HiGHS offers better overall performance than Clp and Cbc, is MIT licensed, and has 3+ years of funded support.