Package cvxpy, add SDP backend

[mkoeppe]

We add cvxpy for disciplined convex programming and extensions.

• cvxpy (​home · ​repo · ​releases · ​PyPI)
• It can call ​many backend solvers -- including most that we currently have as MIP backends, so it may be suitable as a replacement for our homegrown backend code
• Promising route to ​add support for the HiGHS LP/MIP solvers via the ​scipy cython interface to their vendored HiGHS
• supports ​differentiable programming

See also ​cvxpylayers.

Requirements listed in cvxpy's ​setup.py:

python_requires='>=3.6',
install_requires=["osqp >= 0.4.1",
                  "ecos >= 2",
                  "scs >= 1.1.6",
                  "numpy >= 1.15",
                  "scipy >= 1.1.0"],

So the new dependencies are:

• osqp (operator splitting quadratic program) (​home · ​repo · ​PyPI)
• ecos (embedded conic solver) (​repo · ​PyPI)
• SCS (splitting conic solver) (​repo · ​PyPI)

In addition, osqp's ​requirements.txt lists: numpy >= 1.7, scipy >= 0.13.2, qdldl

which adds:

• qldl-python (interface to ​QLDL, to factor quasi-definite linear systems) (​repo · ​PyPI)

Finally, qldl-python depends on pybind11 (already an SPKG)

[slelievre]

New commits:

​dd94452

build/pkgs/cvxpy: New pip package

[dimpase]

can we get some examples/tests using it, too?

[mkoeppe]

Replying to dimpase:

can we get some examples/tests using it, too?

see #31981

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​714ac44	sage.numerical.backends.generic_sdp_backend.{get_solver,default_sdp_solver}: Refactor through new function resolve_sdp_solver
​de29f81	sage.numerical.backends.cvxpy_sdp_backend: New

[git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

​055838b	build/pkgs/cvxpy: New pip package
​001cba1	sage.numerical.backends.generic_sdp_backend.{get_solver,default_sdp_solver}: Refactor through new function resolve_sdp_solver
​22367cb	sage.numerical.backends.cvxpy_sdp_backend: New
​9391d0a	Replace CVXPYSDPBackendFactory by functools.partial

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​8afe7b3

CVXPYSDPBackend.cvxpy_problem: New

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​c701cc2	MatrixSDPBackend._update_problem: New
​19c707a	CVXPYSDPBackend.cvxpy_variables, solve, get_objective_value: New

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​e18f72c

CVXPYSDPBackend: Add more stubs

[mkoeppe]

Ready for a look by an SDP expert...

[git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

​92dd31f	MatrixSDPBackend._update_problem: New
​1850188	build/pkgs/cvxpy: New pip package
​7aae0be	sage.numerical.backends.generic_sdp_backend.{get_solver,default_sdp_solver}: Refactor through new function resolve_sdp_solver
​0ec2ccf	CVXPYSDPBackend.cvxpy_problem: New

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​050bde2

CVXPYSDPBackend.get_variable_value, dual_value: Implement