[WIP] OSQP

[Lucas-Haubert]

Note: Not mergeable until the tests for all backends pass and the code is refactorized.

What is done here:

• Code for dense backend of OSQP.
• Bindings.

To do:

• Pass all the tests for dense backend (eg maros meszaros).
• Code for sparse backend.
• Tests for sparse backend.

In particular for the dense backend:

• Pass the tests (see next section).
• Remove the solved the closest feasible problem option, as not usefull with OSQP (?).
• Remove useless commentaries (once tests pass).
• Remove code duplication (solveDenseQP in the bindings ; init and init_settings in the wrapper ;
• Refactorize the code (once tests pass (?)).
• Benchmarks (once the tests pass).
• Potential engineering tasks (concerning the packaging, or others).

Details on the failing tests:

NOTE: The majority is tested with PrimalDualLDLT and no mu update, as this is the simplest case to be valid. When choosing to update may be more efficient, I did not put the option yet, as some tests are worst with it. Moreover, the algorithm should converge anyway with a fixed value of mu (?).

• Update of mu (rho in OSQP paper) -> some results are worst than without the update, and tests do not pass (eg osqp_dense_qp_solve, test on warm starts) -> make the update of rho more robust (could not find any difference between my implementation and the one from the paper...).
• osqp_cvxpy.cpp: Problems due to memory (more details in commentaries in the file) -> Use of valgrind or another tool ?
  Maros Mezsaros, with the simplest setting (dense backend, PrimalDualLDLT configuration) -> see following points:
• Many tests are skipped (as for ProxQP, since the size of the problem gets above some threshold): should we test them too ? (I guess they were tested previously, but skipped to gain time in the CI or other ?).
• Different categories of errors are listed (algorithm failing to converge with some problems): A general observation is that the polishing step make r_prim and r_dual worst when they: do not converge to 0 sufficiently with the ADMM or seem ok but the dual risudual gap (r_g in the doc) do not converge to 0.
• Errors regarding the memory in some tests, in the polish function in lines 792 (qpwork.k_plus_delta_k_polish = qpwork.k_polish;) or 929 (hat_t = g_polish_rhs;).

[CLAassistant]

All committers have signed the CLA.