Add SDP backend using CVXPY

[mkoeppe]

#34251 adds cvxpy and a MIP backend.

Here we add:

• a new SDP backend.

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 CyLP #33487 package cylp - needed for the CBC backend
• Package ortools #33493 package ortools - provides some more backends

Depends on #33487
Depends on #33504
Depends on #34251

CC: @dimpase @yuan-zhou @sheerluck @dcoudert @seblabbe

Component: linear programming

Work Issues: Rebase on #34251

Author: Matthias Koeppe, Andrey Belgorodski

Branch/Commit: u/mkoeppe/package_cvxpy @ c4462bc

Issue created by migration from https://trac.sagemath.org/ticket/31962

[mkoeppe]

Description changed:

--- 
+++ 
@@ -6,7 +6,31 @@
 
 with differentiable programming - 
 https://www.cvxpy.org/tutorial/advanced/index.html#sensitivity-analysis-and-gradients
+(see also https://github.com/cvxgrp/cvxpylayers)
 
-https://github.com/cvxgrp/cvxpylayers
+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"],
+```
+
+osqp: https://github.com/osqp/osqp-python/blob/master/requirements.txt
+
+```
+numpy >= 1.7
+scipy >= 0.13.2
+qdldl
+```
+
+qdldl: depends on pybind11
+
+ecos: https://github.com/embotech/ecos-python
+
+scs: https://github.com/bodono/scs-python
 
 

[mkoeppe]

Branch: u/mkoeppe/package_cvxpy

[slel]

Description changed:

--- 
+++ 
@@ -1,36 +1,52 @@
-... for disciplined convex programming and extensions
+We add cvxpy for disciplined convex programming and extensions.
 
-https://www.cvxpy.org/index.html
+- cvxpy ([home](https://www.cvxpy.org/)
+  · [repo](https://github.com/cvxpy/cvxpy)
+  · [PyPI](https://pypi.org/project/cvxpy/))
+- can call [many backend solvers](https://www.cvxpy.org/tutorial/advanced/index.html#choosing-a-solver)
+- supports [differentiable programming](https://www.cvxpy.org/tutorial/advanced/index.html#sensitivity-analysis-and-gradients)
 
-with many backend solvers - https://www.cvxpy.org/tutorial/advanced/index.html#choosing-a-solver
+See also [cvxpyplayers](https://github.com/cvxgrp/cvxpylayers).
 
-with differentiable programming - 
-https://www.cvxpy.org/tutorial/advanced/index.html#sensitivity-analysis-and-gradients
-(see also https://github.com/cvxgrp/cvxpylayers)
-
-https://github.com/cvxpy/cvxpy/blob/master/setup.py:
+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"],
+python_requires='>=3.6',
+install_requires=["osqp >= 0.4.1",
+                  "ecos >= 2",
+                  "scs >= 1.1.6",
+                  "numpy >= 1.15",
+                  "scipy >= 1.1.0"],
 ```
 
-osqp: https://github.com/osqp/osqp-python/blob/master/requirements.txt
+So the new dependencies are:
 
-```
-numpy >= 1.7
-scipy >= 0.13.2
-qdldl
-```
+- 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/))
 
-qdldl: depends on pybind11
+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`
 
-ecos: https://github.com/embotech/ecos-python
+which adds:
 
-scs: https://github.com/bodono/scs-python
+- qldl-python (interface
+  to [QLDL](https://github.com/osqp/qdldl), to factor quasi-definite linear systems)
+  ([repo](https://github.com/osqp/qdldl-python)
+  · [PyPI](https://pypi.org/project/qldl/))
 
+Finally, qldl-python depends on pybind11:
 
+- pybind11 (seamless operability between C++11 and Python)
+  ([repo](https://github.com/pybind/pybind11)
+  · [PyPI](https://pypi.org/project/pybind11/)
+  · [docs](https://pybind11.readthedocs.io/))
+

[slel]

New commits:

dd94452

build/pkgs/cvxpy: New pip package

[slel]

Commit: dd94452

[dimpase]

comment:4

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

[mkoeppe]

Description changed:

--- 
+++ 
@@ -43,10 +43,6 @@
   ([repo](https://github.com/osqp/qdldl-python)
   · [PyPI](https://pypi.org/project/qldl/))
 
-Finally, qldl-python depends on pybind11:
+Finally, qldl-python depends on pybind11 (already an SPKG)
 
-- pybind11 (seamless operability between C++11 and Python)
-  ([repo](https://github.com/pybind/pybind11)
-  · [PyPI](https://pypi.org/project/pybind11/)
-  · [docs](https://pybind11.readthedocs.io/))
 

[mkoeppe]

comment:6

Replying to @dimpase:

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

see #31981

[sagetrac-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

[sagetrac-git]

Changed commit from dd94452 to de29f81

[sagetrac-git]

Changed commit from de29f81 to 9391d0a

[sagetrac-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

[sagetrac-git]

Changed commit from 9391d0a to 8afe7b3

[sagetrac-git]

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

8afe7b3

CVXPYSDPBackend.cvxpy_problem: New

[sagetrac-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