Add optional package cvxpy, update cylp, add CVXPY MIP backend

[mkoeppe]

(split out from #31962)

We add cvxpy for disciplined convex programming and extensions as an optional package.

• 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
• PR: CBC.solve_via_data: Work around broken CyLP infeasibility detection cvxpy/cvxpy#1703 - Work around broken CyLP infeasibility detection

We add a new MIP backend solver="CVXPY". Using solver="CVXPY/ECOS", solver="CVXPY/GLPK", etc., CVXPY can be asked to use a specific solver.

When also cylp is installed (from #33487, upgraded here), the new solver backend "CVXPY/CBC" becomes the default (unless Gurobi or CPLEX are available), thus replacing the similar functionality of the CBC backend provided by sage_numerical_backend_coin.

Details about dependencies: 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 QDLDL, to factor quasi-definite linear systems) (repo · PyPI)

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

See also:

• Meta-ticket: Use Python optimization interfaces: CVXPY, SCIP, or-tools, PuLP, Pyomo, cylp... #26511 Meta-ticket: Use Python optimization interfaces: PuLP, Pyomo, cylp...
• Package ortools #33493 package ortools - provides some more backends

Follow-ups:

• Upgrade optional package cbc to 2.10.x, remove sage_numerical_backends_coin #30644 Remove sage_numerical_backends_coin, Upgrade optional package cbc to 2.10.7

Depends on #34228

CC: @dimpase @yuan-zhou @sheerluck @dcoudert @seblabbe @maxale @kiwifb @isuruf @tkralphs

Component: packages: optional

Author: Matthias Koeppe, Andrey Belgorodski

Reviewer: Martin Pépin

Issue created by migration from https://trac.sagemath.org/ticket/34251

[mkoeppe]

Branch: u/mkoeppe/add_optional_package_cvxpy

[mkoeppe]

Description changed:

--- 
+++ 
@@ -1 +1,2 @@
 (split out from #31962)
+

[mkoeppe]

Commit: 76d1208

[mkoeppe]

Last 10 new commits:

cff440e	adding some code from ppl_backend.pyx to cvxpy_backend.{pyx,pxd}
8c6f323	CVXPYBackend.is_variable_{boolean,integer,continuous}: Implement
b497afc	src/sage/numerical/backends/cvxpy_backend.pyx: Fix up some doctests
942d2ed	CVXPYBackend.objective_coefficient: Fix up
5a5ab69	build/pkgs/cylp: Add patch from https://github.com/coin-or/CyLP/pull/150
75f867d	build/pkgs/cvxpy: Use https://github.com/cvxpy/cvxpy/pull/1707
1fb2926	build/pkgs/cylp: Add another commit from https://github.com/coin-or/CyLP/pull/150
4fd763a	src/sage/numerical/backends/cvxpy_backend_test.py: New
8e482be	build/pkgs/cylp: Update to 0.91.5, remove patches
76d1208	build/pkgs/cvxpy/requirements.txt: Update git ref

[mkoeppe]

Changed author from Matthias Koeppe to Matthias Koeppe, Andrey Belgorodski

[mkoeppe]

Description changed:

--- 
+++ 
@@ -1,2 +1,60 @@
 (split out from #31962)
 
+We add `cvxpy` for disciplined convex programming and extensions as an optional package.
+
+- cvxpy ([home](https://www.cvxpy.org/)
+  · [repo](https://github.com/cvxpy/cvxpy)
+  · [releases](https://github.com/cvxpy/cvxpy/releases)
+  · [PyPI](https://pypi.org/project/cvxpy/))
+- It can call [many backend solvers](https://www.cvxpy.org/tutorial/advanced/index.html#choosing-a-solver) -- 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](https://github.com/cvxpy/cvxpy/issues/1443) via the [scipy cython interface to their vendored HiGHS](https://github.com/scipy/scipy/issues/14455)
+- supports [differentiable programming](https://www.cvxpy.org/tutorial/advanced/index.html#sensitivity-analysis-and-gradients)
+- PR: https://github.com/cvxpy/cvxpy/pull/1703 - Work around broken CyLP infeasibility detection
+
+When `cylp` is installed (from #33487, upgraded here), a new solver backend `"CVXPY/CBC"` becomes the default (unless Gurobi or CPLEX are available). This replaces 
+
+
+Details about dependencies: Requirements listed in
+cvxpy's [setup.py](https://github.com/cvxpy/cvxpy/blob/master/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](https://osqp.org/)
+  · [repo](https://github.com/osqp/osqp-python)
+  · [PyPI](https://pypi.org/project/osqp/))
+- ecos (embedded conic solver)
+  ([repo](https://github.com/embotech/ecos-python)
+  · [PyPI](https://pypi.org/project/ecos/))
+- SCS (splitting conic solver)
+  ([repo](https://github.com/bodono/scs-python)
+  · [PyPI](https://pypi.org/project/scs/))
+
+In addition, osqp's [requirements.txt](https://github.com/osqp/osqp-python/blob/master/requirements.txt) lists:
+`numpy >= 1.7`, `scipy >= 0.13.2`, `qdldl`
+
+which adds:
+
+- qldl-python (interface
+  to [QDLDL](https://github.com/osqp/qdldl), to factor quasi-definite linear systems)
+  ([repo](https://github.com/osqp/qdldl-python)
+  · [PyPI](https://pypi.org/project/qdldl/))
+
+Finally, qldl-python depends on pybind11 (already an SPKG)
+
+See also:
+- #26511 Meta-ticket: Use Python optimization interfaces: PuLP, Pyomo, cylp...
+- #33493 package ortools - provides some more backends
+
+Follow-ups:
+- #30644 Remove `sage_numerical_backends_coin`, Upgrade optional package cbc to 2.10.7
+

[sagetrac-git]

Changed commit from 76d1208 to 7d4dccb

[sagetrac-git]

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

7d4dccb

build/pkgs/cvxpy: Make it a normal package, add dependencies qdldl_python, osqp, scs, ecos

[mkoeppe]

Description changed:

--- 
+++ 
@@ -11,7 +11,7 @@
 - supports [differentiable programming](https://www.cvxpy.org/tutorial/advanced/index.html#sensitivity-analysis-and-gradients)
 - PR: https://github.com/cvxpy/cvxpy/pull/1703 - Work around broken CyLP infeasibility detection
 
-When `cylp` is installed (from #33487, upgraded here), a new solver backend `"CVXPY/CBC"` becomes the default (unless Gurobi or CPLEX are available). This replaces 
+When `cylp` is installed (from #33487, upgraded here), a new solver backend `"CVXPY/CBC"` becomes the default (unless Gurobi or CPLEX are available). This replaces the backend provided by `sage_numerical_backend_coin`
 
 
 Details about dependencies: Requirements listed in

[sagetrac-git]

Changed commit from 7d4dccb to aab359f

[sagetrac-git]

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

aab359f

build/pkgs/{ecos,osqp}_python: Renamed from ecos, osqp

[sagetrac-git]

Changed commit from aab359f to 6d039ae

[sagetrac-git]

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

468b2c5	build/pkgs/ecos_python/dependencies: Add suitesparse
6d039ae	build/pkgs/{ecos,osqp}_python: Use --no-build-isolation

[sagetrac-git]

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

763985d

src/sage/numerical/backends/cvxpy_backend.pyx: Make doctests pass

[sagetrac-git]

Changed commit from 6d039ae to 763985d