sedumipy

A MATLAB/Octave-free Python port of SeDuMi — an interior-point solver for linear (LP), second-order cone (SOCP), and semidefinite (SDP) programs — as a standalone C kernel library plus a Python (NumPy/SciPy) package. No MATLAB or GNU Octave runtime is needed to install or run it.

It solves conic programs over a symmetric cone K — one call gives you both sides of the primal-dual pair:

\begin{aligned}
\text{(P)} \quad \min_{x} \;\; & c^\top x
  & \qquad \text{(D)} \quad \max_{y,\,s} \;\; & b^\top y \\
\text{s.t.} \;\; & Ax = b, \;\; x \in K
  & \qquad \text{s.t.} \;\; & A^\top y + s = c, \;\; s \in K^{*}
\end{aligned}

K is a product of blocks of five kinds — free, nonnegative orthant, second-order (Lorentz), rotated Lorentz, and positive semidefinite — so LP, SOCP, and SDP are the cases where every block is of one kind, and a single problem may mix them freely. An LP, for instance:

import numpy as np
import sedumipy

# minimize    7*x1 + 4*x2 + 10*x3
# subject to  3*x1 + 1*x2 +  2*x3 = 9
#             1*x1 + 2*x2 +  4*x3 = 8
#             x1, x2, x3 >= 0
A = np.array([[3.0, 1.0, 2.0],      # one row per equality constraint
              [1.0, 2.0, 4.0]])
b = np.array([9.0, 8.0])            # their right-hand sides
c = np.array([7.0, 4.0, 10.0])      # objective coefficients
K = {"l": 3}                        # all 3 variables are >= 0

x, y, info = sedumipy.sedumi(A, b, c, K)
# x = [2., 3., 0.]   the optimum, costing c @ x = 26

Here x is the primal optimum and y the dual one; K = {"l": 3} says all three variables are nonnegative. This mirrors original SeDuMi's own [x, y, info] = sedumi(A, b, c, K) call.

The usage guide defines each cone and works a mixed LP + SOCP + SDP model end to end, from the written constraints down to A, b, c, and K.

New contributor? Read CONTRIBUTING.md first — it has the current phase-by-phase status, the porting workflow this project follows, known scope limitations, and the prioritized list of remaining work.

Status

LP, second-order-cone (SOCP), and semidefinite (SDP, K.s) problems are all fully ported and verified against original Octave/SeDuMi output, to tight numerical tolerances, including on published SDPLIB and DIMACS benchmark problems (see Benchmarks below). Dense-column preconditioning is also implemented. Wheels are published to PyPI for Linux (manylinux), macOS and Windows by wheels.yml's cibuildwheel job (the Windows build uses an MSYS2/MinGW toolchain and has only been exercised on GitHub Actions' hosted runner, not hand-verified on a real Windows machine) — see CONTRIBUTING.md for the full phase-by-phase status and known limitations.

Use it from cvxpy

Problems can also be written in cvxpy's modeling language rather than as (A, b, c, K) by hand — install cvxpy alongside sedumipy (pip install sedumipy[cvxpy]) and hand solve() an instance of the solver class:

import cvxpy as cp
from sedumipy.cvxpy_interface import SEDUMIPY

x = cp.Variable(3)
problem = cp.Problem(cp.Minimize(c @ x), [A @ x == b, x >= 0])
problem.solve(solver=SEDUMIPY())   # 26.0, with the same A, b, c as above

A stock cvxpy install is enough (this uses cvxpy's own custom-solver hook — nothing has to be merged into cvxpy for it to work), and it covers the same LP/SOCP/SDP scope the solver itself does. See the usage guide for solver options, dual values, and what is out of scope.

Installation

pip install sedumipy

Wheels cover CPython 3.10-3.13 on Linux x86_64 (manylinux), Windows x64 and macOS (Apple silicon), with the compiled kernel library and its BLAS already inside them — no compiler, no BLAS install, no MATLAB or Octave. Anything else falls back to the source distribution and compiles locally, which does need a toolchain: see docs/installation.rst.

Documentation

Full documentation (installation, the problem/solver API, and the internals reference) is published at napinoco.github.io/sedumipy (built with Sphinx from docs/, auto-published to GitHub Pages by .github/workflows/docs.yml on every push to main). To build it locally instead:

pip install -r docs/requirements.txt
sphinx-build -b html docs docs/_build/html

Repository layout

The original MATLAB/Octave/MEX implementation this project ports from is kept as a reference-only git submodule, pinned to the commit the port started from:

sedumipy/
  vendor/sedumi-upstream/   # submodule: sqlp/sedumi (reference only, not built by default)
  examples/sdplib/          # submodule: vsdp/SDPLIB (published benchmark problems + optimal values)
  examples/dimacs/          # submodule: vsdp/DIMACS (published benchmark problems + optimal values)
  csrc/                     # forked, MEX-free standalone C kernels (source for libsedumi.so)
  src/sedumipy/             # the Python package
  tests/                    # test suite + committed Octave-generated oracle fixtures
  tools/                    # libsedumi build script + oracle/golden-reference generators
  docs/                     # Sphinx documentation source

Getting started from a checkout

To work on sedumipy itself (rather than just use it — see Installation above):

git clone --recurse-submodules <this-repo-url>
cd sedumipy
python -m venv .venv
.venv/bin/pip install -e .[test]
.venv/bin/python -m pytest tests/ -q

If you already cloned without --recurse-submodules, run git submodule update --init --recursive first. Building libsedumi.so (the compiled C kernel library) requires a C compiler (e.g. apt install build-essential on Debian/Ubuntu, or nothing extra at all on macOS — Xcode's command line tools provide cc; on Windows, install MSYS2 and its mingw-w64-x86_64-gcc package first — see the Windows note in docs/installation.rst or CONTRIBUTING.md); it's then built automatically the first time sedumipy is imported, via tools/build_libsedumi.sh. It also needs a BLAS. On macOS this is always the system Accelerate framework — nothing to install. On Linux/Windows, run pip install scipy-openblas64==0.3.34.106.0 (a pip-installable, prebuilt BLAS with wheels for both — the same, version-pinned one the published wheels themselves link, see pyproject.toml's [tool.cibuildwheel] comment for why it's pinned) before pip install -e .[test] --no-build-isolation above, or skip that and it falls back to a system BLAS per OS instead (e.g. apt install libopenblas-dev on Linux) — see docs/installation.rst for the full story. The Octave submodule is only needed to regenerate oracle/golden- reference data, not to run the existing test suite.

Benchmarks

tests/test_benchmarks.py solves published SDPLIB and DIMACS problems (added as git submodules under examples/) and checks the result against each collection's own official optimal-value table -- a correctness/regression check against real reference numbers, not a synthetic self-check. It also prints a timing/iteration-count summary and writes it to benchmark_results.csv.

Coverage is essentially the full published set: all 92 SDPLIB problems and every DIMACS problem sedumi() can read directly, minus a documented handful this port can't yet solve in bounded time/memory or that hit a real solver limitation -- see the module's own docstring for the full exclusion list and why each one is excluded.

git submodule update --init --recursive   # if not already done
.venv/bin/python -m pytest tests/test_benchmarks.py -v          # everything, ~101 problems (~10 min)
.venv/bin/python -m pytest tests/test_benchmarks.py -v -m mini  # fastest subset only (~35s)

Problems are grouped by pytest.mark.mini (<2s each) / timing (2-20s) / extended (20s-130s) by measured solve time -- see the module's own docstring for the sign conventions each collection/family needs.

A note on citation and attribution

sedumipy is an independent, unofficial re-implementation of SeDuMi, created without involvement from the original SeDuMi authors or maintainers. Although it aims to reproduce SeDuMi's numerical behavior faithfully, it is a from-scratch port and may differ from the original in ways not yet identified — in short, it may not always behave identically to the original SeDuMi.

If you use this software in research, please cite the original SeDuMi paper to give credit where it is due:

Sturm, J.F. (1999). Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optimization Methods and Software, 11(1-4), 625-653.

At the same time, please make clear in your own work that results were produced using sedumipy, an unofficial Python port — not the original SeDuMi. Any discrepancy, bug, or unexpected numerical behavior you observe here is a property of this port, not of SeDuMi itself, and should not be attributed to the original project or its authors.

License

SeDuMi is licensed under the GNU General Public License v2 (see LICENSE); this port, being a derivative work, is licensed the same way.