newton-sos

Damped Newton method to solve low-rank problems arising from KernelSOS and Sum-of-Squares relaxations

Goal

The newton_sos package provides a Python interface to solve large-scale semidefinite programs (SDPs) that arise from Kernel Sum-of-Squares (KernelSOS) and Sum-of-Squares (SOS) relaxations. The core of the package is implemented in Rust for performance, while Python bindings are provided for ease of use.

Formally, the package aims to solve SDPs of the form: $$\max_{c\in\mathbb{R}, B \in \mathbb{S}^n_+} c - \lambda \text{Tr}(B) + t \log \det (B) \quad \text{s.t. }\quad f_i - c = \Phi_i^T B \Phi_i, ::\forall i\in[![1, N]!]$$ where $\Phi_i$ are feature vectors derived from a chosen kernel function, and $f_i$ are given function evaluations at points $x_i$.

Basic usage

The steps to solve an SDP using the Python bindings are similar to the Rust version. First, define a problem by creating an instance of the Problem class. Then, compute the kernel matrix using the initialize_native_kernel method with the desired kernel parameters. Finally, call the solve method on the Problem instance to solve the optimization problem:

problem = Problem( ... )  # Define the problem
problem.initialize_native_kernel( ... )  # Compute the kernel matrix
result = problem.solve( ... )  # Solve the optimization problem

Full example

The example below demonstrates how to use the newton_sos package to solve a toy polynomial optimization problem.

import numpy as np
from newton_sos import Problem
from newton_sos import solve

# Number of sample points, which defines the size of the problem
n = 10


# Define the polynomial function to optimize
def polynomial(x):
    return x**4 - 3 * x**3 + 2 * x**2 + x - 1


# Generate sample points and evaluate the polynomial at those points
x_samples = np.array([[-2 + i * 0.5] for i in range(n)], dtype=np.float64)
f_samples = np.array([[polynomial(x[0])] for x in x_samples], dtype=np.float64)
# note that the data type must be float64

# Create the optimization problem
problem = Problem(0.01, 0.1 / n, x_samples, f_samples)
# Initialize the kernel matrix
problem.initialize_native_kernel("laplacian", 0.1)
# here, we chose a Laplacian kernel with bandwidth 0.1

# Run the solver
solve_result = solve(problem, max_iter=100, verbose=True, method="partial_piv_lu")

# Extract the solution
assert solve_result.converged
assert solve_result.iterations == 10
assert solve_result.status == "Converged in Newton decrement"
assert abs(solve_result.z_hat[0, 0] - 0.01939745) < 1e-7
print(f"Result: {solve_result.z_hat[0, 0]}")

Citing

If you use this code in your research, please use the following citation:

@software{newton_sos,
  author = {Groudiev, Antoine},
  title = {{Newton-SOS}: Damped Newton method to solve low-rank problems arising from KernelSOS and Sum-of-Squares relaxations},
  url = {https://github.com/agroudiev/newton-sos},
  version = {0.2.2},
  date = {2025-12-22},
}

Project links

Data verified by PyPI on May 1, 2026
Data provided by the project maintainers, verified at the time the release was uploaded to PyPI.

Key dates

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  • Released:
Latest release

1 maintainer

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Avatar for agroudiev from gravatar.com agroudiev

Credits

Author: Antoine Groudiev

GitHub Statistics

Data verified by PyPI on May 1, 2026
The GitHub source repository was provided by the project maintainers and verified by PyPI at the time of upload. Stars, forks, and open issues/PRs are derived from that repository and have not been independently verified.

Requires

Python >=3.8

Classifiers

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Metadata

Project links

Data verified by PyPI on May 1, 2026
Data provided by the project maintainers, verified at the time the release was uploaded to PyPI.

Key dates

PyPI data
Data sourced directly from PyPI's database.
  • Released:
Latest release

1 maintainer

PyPI data
Data sourced directly from PyPI's database.
Avatar for agroudiev from gravatar.com agroudiev

Credits

Author: Antoine Groudiev

GitHub Statistics

Data verified by PyPI on May 1, 2026
The GitHub source repository was provided by the project maintainers and verified by PyPI at the time of upload. Stars, forks, and open issues/PRs are derived from that repository and have not been independently verified.

Requires

Python >=3.8

Classifiers

Report project as malware

Release files for newton-sos 0.2.3

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Source distribution for newton-sos 0.2.3
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Table of built distributions (wheels) for newton-sos 0.2.3
File
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newton_sos-0.2.3-pp310-pypy310_pp73-manylinux_2_17_armv7l.manylinux2014_armv7l.whl 618.0 kB PyPy 3.10 PyPy 3.10 7.3 Linux glibc 2.17+ ARMv7l Details
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newton_sos-0.2.3-pp39-pypy39_pp73-manylinux_2_17_s390x.manylinux2014_s390x.whl 681.4 kB PyPy 3.9 PyPy 3.9 7.3 Linux glibc 2.17+ IBM System/390x Details
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newton_sos-0.2.3-cp313-cp313t-manylinux_2_17_armv7l.manylinux2014_armv7l.whl 610.3 kB CPython 3.13 CPython 3.13 free-threading Linux glibc 2.17+ ARMv7l Details
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newton_sos-0.2.3-cp313-cp313-manylinux_2_17_armv7l.manylinux2014_armv7l.whl 609.5 kB CPython 3.13 CPython 3.13 Linux glibc 2.17+ ARMv7l Details
newton_sos-0.2.3-cp313-cp313-manylinux_2_17_aarch64.manylinux2014_aarch64.whl 731.1 kB CPython 3.13 CPython 3.13 Linux glibc 2.17+ ARM64 Details
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newton_sos-0.2.3-cp312-cp312-manylinux_2_17_s390x.manylinux2014_s390x.whl 670.5 kB CPython 3.12 CPython 3.12 Linux glibc 2.17+ IBM System/390x Details
newton_sos-0.2.3-cp312-cp312-manylinux_2_17_ppc64le.manylinux2014_ppc64le.whl 804.5 kB CPython 3.12 CPython 3.12 Linux glibc 2.17+ PowerPC 64-le Details
newton_sos-0.2.3-cp312-cp312-manylinux_2_17_armv7l.manylinux2014_armv7l.whl 610.3 kB CPython 3.12 CPython 3.12 Linux glibc 2.17+ ARMv7l Details
newton_sos-0.2.3-cp312-cp312-manylinux_2_17_aarch64.manylinux2014_aarch64.whl 731.8 kB CPython 3.12 CPython 3.12 Linux glibc 2.17+ ARM64 Details
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newton_sos-0.2.3-cp311-cp311-manylinux_2_17_s390x.manylinux2014_s390x.whl 678.5 kB CPython 3.11 CPython 3.11 Linux glibc 2.17+ IBM System/390x Details
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newton_sos-0.2.3-cp311-cp311-manylinux_2_17_aarch64.manylinux2014_aarch64.whl 732.6 kB CPython 3.11 CPython 3.11 Linux glibc 2.17+ ARM64 Details
newton_sos-0.2.3-cp311-cp311-macosx_11_0_arm64.whl 624.5 kB CPython 3.11 CPython 3.11 macOS 11.0+ ARM64 Details
newton_sos-0.2.3-cp311-cp311-macosx_10_12_x86_64.whl 941.6 kB CPython 3.11 CPython 3.11 macOS 10.12+ x86-64 Details
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newton_sos-0.2.3-cp310-cp310-manylinux_2_17_s390x.manylinux2014_s390x.whl 678.4 kB CPython 3.10 CPython 3.10 Linux glibc 2.17+ IBM System/390x Details
newton_sos-0.2.3-cp310-cp310-manylinux_2_17_ppc64le.manylinux2014_ppc64le.whl 810.2 kB CPython 3.10 CPython 3.10 Linux glibc 2.17+ PowerPC 64-le Details
newton_sos-0.2.3-cp310-cp310-manylinux_2_17_armv7l.manylinux2014_armv7l.whl 614.5 kB CPython 3.10 CPython 3.10 Linux glibc 2.17+ ARMv7l Details
newton_sos-0.2.3-cp310-cp310-manylinux_2_17_aarch64.manylinux2014_aarch64.whl 732.9 kB CPython 3.10 CPython 3.10 Linux glibc 2.17+ ARM64 Details
newton_sos-0.2.3-cp39-cp39-manylinux_2_17_x86_64.manylinux2014_x86_64.whl 1.1 MB CPython 3.9 CPython 3.9 Linux glibc 2.17+ x86-64 Details
newton_sos-0.2.3-cp39-cp39-manylinux_2_17_s390x.manylinux2014_s390x.whl 680.2 kB CPython 3.9 CPython 3.9 Linux glibc 2.17+ IBM System/390x Details
newton_sos-0.2.3-cp39-cp39-manylinux_2_17_ppc64le.manylinux2014_ppc64le.whl 812.6 kB CPython 3.9 CPython 3.9 Linux glibc 2.17+ PowerPC 64-le Details
newton_sos-0.2.3-cp39-cp39-manylinux_2_17_armv7l.manylinux2014_armv7l.whl 617.2 kB CPython 3.9 CPython 3.9 Linux glibc 2.17+ ARMv7l Details
newton_sos-0.2.3-cp39-cp39-manylinux_2_17_aarch64.manylinux2014_aarch64.whl 735.2 kB CPython 3.9 CPython 3.9 Linux glibc 2.17+ ARM64 Details
newton_sos-0.2.3-cp38-cp38-manylinux_2_17_x86_64.manylinux2014_x86_64.whl 1.1 MB CPython 3.8 CPython 3.8 Linux glibc 2.17+ x86-64 Details
newton_sos-0.2.3-cp38-cp38-manylinux_2_17_s390x.manylinux2014_s390x.whl 680.4 kB CPython 3.8 CPython 3.8 Linux glibc 2.17+ IBM System/390x Details
newton_sos-0.2.3-cp38-cp38-manylinux_2_17_ppc64le.manylinux2014_ppc64le.whl 812.4 kB CPython 3.8 CPython 3.8 Linux glibc 2.17+ PowerPC 64-le Details
newton_sos-0.2.3-cp38-cp38-manylinux_2_17_armv7l.manylinux2014_armv7l.whl 617.0 kB CPython 3.8 CPython 3.8 Linux glibc 2.17+ ARMv7l Details
newton_sos-0.2.3-cp38-cp38-manylinux_2_17_aarch64.manylinux2014_aarch64.whl 735.7 kB CPython 3.8 CPython 3.8 Linux glibc 2.17+ ARM64 Details

Total release size: 50.2 MB

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