nlpql

NLPQL

Non-Linear Programming by Quadratic Lagrangian (NLPQL) for Python

nlpql solves the smooth nonlinear programming problem

min  f(x)
     g_j(x)  = 0 ,  j = 1, ..., me
     g_j(x) >= 0 ,  j = me+1, ..., m
     xl <= x <= xu

by a sequential quadratic programming method. A quadratic subproblem is formulated from a quadratic approximation of the Lagrangian and a linearization of the constraints, and the steplength is determined by a line search with respect to an augmented Lagrangian merit function. Data fitting, min-max and multicriteria problems are transformed into programs of this form and solved by the same algorithm.

Available codes

Nonlinear programming

code	purpose
`NLPQLP`	distributed and non-monotone line search, internal restarts
`NLPQL`	the original SQP method
`NLPQLY`	easy-to-use, all derivatives approximated internally
`NLPQLB`	active set strategy for a very large number of constraints
`NLPQLG`	successive restarts for a stepwise improvement of local minima
`NLPQLF`	model functions evaluable only on a convex subset

Data fitting and multicriteria optimization

Every code of this group transforms its problem into a nonlinear program of the form above and solves it with NLPQLP.

code	purpose
`NLPLSQ`	constrained nonlinear least squares
`NLPLSX`	least squares with a very large number of terms
`NLPL1`	sum of absolute values
`NLPINF`	maximum norm data fitting
`NLPMMX`	min-max optimization
`NLPJOB`	multicriteria optimization, sixteen scalar transformations

Quadratic programming

code	purpose
`QL`	convex quadratic programming, solves the subproblem of every SQP step

Quick example

Rosenbrock's post office problem, test problem TP37 of Hock and Schittkowski:

import numpy as np
from nlpql import minimize

res = minimize(
    fun=lambda x: -x[0] * x[1] * x[2],
    x0=[10.0, 10.0, 10.0],
    jac=lambda x: np.array([-x[1] * x[2], -x[0] * x[2], -x[0] * x[1]]),
    bounds=[(0.0, 42.0)] * 3,
    constraints={
        "type": "ineq",
        "fun": lambda x: np.array([
            x[0] + 2 * x[1] + 2 * x[2],
            72 - x[0] - 2 * x[1] - 2 * x[2],
        ]),
        "jac": lambda x: np.array([[1.0, 2.0, 2.0], [-1.0, -2.0, -2.0]]),
    },
)

print(res.x)  # [24. 12. 12.]
print(res.fun)  # -3456.0

Problems with a very large number of constraints are handled by the active set code, which only needs the gradients of a working set:

m = 200_000
y = np.arange(m) / (m - 1.0)

res = minimize(
    fun=lambda x: float(np.sum(np.exp(x))),
    x0=[1.0, 0.5, 0.0],
    method="NLPQLB",
    jac=np.exp,
    bounds=[(-100.0, 100.0)] * 3,
    constraints={
        "type": "ineq",
        "fun": lambda x: x[0] + x[1] * y + x[2] * y**2 - 1.0 / (1.0 + y**2),
        "jac": lambda x: np.column_stack([np.ones_like(y), y, y**2]),
    },
    options={"mw": 420, "acc": 1e-10, "rho": 0.1},
)
print(res.fun)  # 4.3011838

Features

upper and lower bounds are handled separately and stay satisfied
an additional variable prevents inconsistent linearized constraints
non-monotone line search and automatic restarts make the method very stable for noisy function and derivative values
objective and constraints may be evaluated simultaneously at several test points of the line search
initial multipliers and an initial quasi-Newton matrix may be provided
reverse communication, so the model functions can be supplied by an external simulation
no COMMON blocks, no SAVE, no memory allocation, therefore thread-safe and re-entrant
the detailed iteration protocol of the original codes is available through options={"iprint": 4}

Installation

pip install nlpql

Requires Python 3.10+ and NumPy. No external runtime dependencies. See the full installation guide for uv, poetry and source builds.

Documentation

Theory — the mathematics of the implemented algorithms
Quickstart — runnable examples
API Reference — functions, options and termination flags
References — literature citations

Provenance

The algorithms were developed by Prof. Dr. K. Schittkowski and co-authors. The sources in this repository were written from scratch from the published user's guides and papers; no source code of the original implementations was used. Subroutine and argument names follow the published documentation, so existing calling programs can be adapted easily. Reimplementation from the documentation was explicitly permitted by the copyright holder.

License

GNU General Public License v3 (GPLv3) — see LICENSE.

Metadata

Release files for nlpql 0.2.1

For a detailed explanation of source distributions (sdists) and built distributions (wheels), please see the package formats documentation.

Built distributions (wheels)

Table of built distributions (wheels) for nlpql 0.2.1
File	Interpreter	ABI	Platform	Reset
nlpql-0.2.1-cp315-cp315t-win_amd64.whl 366.0 kB Aug 19, 2026	CPython 3.15	CPython 3.15 free-threading	Windows x86-64	Details
nlpql-0.2.1-cp315-cp315t-musllinux_1_2_x86_64.whl 1.5 MB Aug 19, 2026	CPython 3.15	CPython 3.15 free-threading	Linux musl 1.2+ x86-64	Details
nlpql-0.2.1-cp315-cp315t-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl 1.1 MB Aug 19, 2026	CPython 3.15	CPython 3.15 free-threading	Linux glibc 2.27+ x86-64, Linux glibc 2.28+ x86-64	Details
nlpql-0.2.1-cp315-cp315t-macosx_15_0_arm64.whl 878.1 kB Aug 19, 2026	CPython 3.15	CPython 3.15 free-threading	macOS 15.0+ ARM64	Details
nlpql-0.2.1-cp315-cp315-win_amd64.whl 365.0 kB Aug 19, 2026	CPython 3.15	CPython 3.15	Windows x86-64	Details
nlpql-0.2.1-cp315-cp315-musllinux_1_2_x86_64.whl 1.5 MB Aug 19, 2026	CPython 3.15	CPython 3.15	Linux musl 1.2+ x86-64	Details
nlpql-0.2.1-cp315-cp315-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl 1.1 MB Aug 19, 2026	CPython 3.15	CPython 3.15	Linux glibc 2.28+ x86-64, Linux glibc 2.27+ x86-64	Details
nlpql-0.2.1-cp315-cp315-macosx_15_0_arm64.whl 877.5 kB Aug 19, 2026	CPython 3.15	CPython 3.15	macOS 15.0+ ARM64	Details
nlpql-0.2.1-cp314-cp314t-win_amd64.whl 366.0 kB Aug 19, 2026	CPython 3.14	CPython 3.14 free-threading	Windows x86-64	Details
nlpql-0.2.1-cp314-cp314t-musllinux_1_2_x86_64.whl 1.5 MB Aug 19, 2026	CPython 3.14	CPython 3.14 free-threading	Linux musl 1.2+ x86-64	Details
nlpql-0.2.1-cp314-cp314t-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl 1.1 MB Aug 19, 2026	CPython 3.14	CPython 3.14 free-threading	Linux glibc 2.27+ x86-64, Linux glibc 2.28+ x86-64	Details
nlpql-0.2.1-cp314-cp314t-macosx_15_0_arm64.whl 878.1 kB Aug 19, 2026	CPython 3.14	CPython 3.14 free-threading	macOS 15.0+ ARM64	Details
nlpql-0.2.1-cp314-cp314-win_amd64.whl 365.0 kB Aug 19, 2026	CPython 3.14	CPython 3.14	Windows x86-64	Details
nlpql-0.2.1-cp314-cp314-musllinux_1_2_x86_64.whl 1.5 MB Aug 19, 2026	CPython 3.14	CPython 3.14	Linux musl 1.2+ x86-64	Details
nlpql-0.2.1-cp314-cp314-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl 1.1 MB Aug 19, 2026	CPython 3.14	CPython 3.14	Linux glibc 2.27+ x86-64, Linux glibc 2.28+ x86-64	Details
nlpql-0.2.1-cp314-cp314-macosx_15_0_arm64.whl 877.5 kB Aug 19, 2026	CPython 3.14	CPython 3.14	macOS 15.0+ ARM64	Details
nlpql-0.2.1-cp313-cp313-win_amd64.whl 357.5 kB Aug 19, 2026	CPython 3.13	CPython 3.13	Windows x86-64	Details
nlpql-0.2.1-cp313-cp313-musllinux_1_2_x86_64.whl 1.5 MB Aug 19, 2026	CPython 3.13	CPython 3.13	Linux musl 1.2+ x86-64	Details
nlpql-0.2.1-cp313-cp313-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl 1.1 MB Aug 19, 2026	CPython 3.13	CPython 3.13	Linux glibc 2.27+ x86-64, Linux glibc 2.28+ x86-64	Details
nlpql-0.2.1-cp313-cp313-macosx_15_0_arm64.whl 877.5 kB Aug 19, 2026	CPython 3.13	CPython 3.13	macOS 15.0+ ARM64	Details
nlpql-0.2.1-cp312-cp312-win_amd64.whl 357.5 kB Aug 19, 2026	CPython 3.12	CPython 3.12	Windows x86-64	Details
nlpql-0.2.1-cp312-cp312-musllinux_1_2_x86_64.whl 1.5 MB Aug 19, 2026	CPython 3.12	CPython 3.12	Linux musl 1.2+ x86-64	Details
nlpql-0.2.1-cp312-cp312-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl 1.1 MB Aug 19, 2026	CPython 3.12	CPython 3.12	Linux glibc 2.28+ x86-64, Linux glibc 2.27+ x86-64	Details
nlpql-0.2.1-cp312-cp312-macosx_15_0_arm64.whl 877.5 kB Aug 19, 2026	CPython 3.12	CPython 3.12	macOS 15.0+ ARM64	Details
nlpql-0.2.1-cp311-cp311-win_amd64.whl 357.1 kB Aug 19, 2026	CPython 3.11	CPython 3.11	Windows x86-64	Details
nlpql-0.2.1-cp311-cp311-musllinux_1_2_x86_64.whl 1.5 MB Aug 19, 2026	CPython 3.11	CPython 3.11	Linux musl 1.2+ x86-64	Details
nlpql-0.2.1-cp311-cp311-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl 1.1 MB Aug 19, 2026	CPython 3.11	CPython 3.11	Linux glibc 2.28+ x86-64, Linux glibc 2.27+ x86-64	Details
nlpql-0.2.1-cp311-cp311-macosx_15_0_arm64.whl 876.9 kB Aug 19, 2026	CPython 3.11	CPython 3.11	macOS 15.0+ ARM64	Details
nlpql-0.2.1-cp310-cp310-win_amd64.whl 357.5 kB Aug 19, 2026	CPython 3.10	CPython 3.10	Windows x86-64	Details
nlpql-0.2.1-cp310-cp310-musllinux_1_2_x86_64.whl 1.5 MB Aug 19, 2026	CPython 3.10	CPython 3.10	Linux musl 1.2+ x86-64	Details
nlpql-0.2.1-cp310-cp310-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl 1.1 MB Aug 19, 2026	CPython 3.10	CPython 3.10	Linux glibc 2.28+ x86-64, Linux glibc 2.27+ x86-64	Details
nlpql-0.2.1-cp310-cp310-macosx_15_0_arm64.whl 874.6 kB Aug 19, 2026	CPython 3.10	CPython 3.10	macOS 15.0+ ARM64	Details

Total release size: 30.9 MB

Release files / nlpql-0.2.1-cp315-cp315t-win_amd64.whl

Download URL	nlpql-0.2.1-cp315-cp315t-win_amd64.whl
Size	366.0 kB
Tags	CPython 3.15 CPython 3.15 free-threading Windows x86-64
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Release files / nlpql-0.2.1-cp315-cp315t-musllinux_1_2_x86_64.whl

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Release files / nlpql-0.2.1-cp315-cp315t-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl

Download URL	nlpql-0.2.1-cp315-cp315t-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl
Size	1.1 MB
Tags	CPython 3.15 CPython 3.15 free-threading Linux glibc 2.27+ x86-64 Linux glibc 2.28+ x86-64
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Publishing repository: github.com/eggzec/nlpql
Publishing commit: github.com/eggzec/nlpql/tree/ff1f4425c10d709cde345970725c208763f1320a

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Release files / nlpql-0.2.1-cp315-cp315t-macosx_15_0_arm64.whl

Download URL	nlpql-0.2.1-cp315-cp315t-macosx_15_0_arm64.whl
Size	878.1 kB
Tags	CPython 3.15 CPython 3.15 free-threading macOS 15.0+ ARM64
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Release files / nlpql-0.2.1-cp315-cp315-win_amd64.whl

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Release files / nlpql-0.2.1-cp315-cp315-musllinux_1_2_x86_64.whl

Download URL	nlpql-0.2.1-cp315-cp315-musllinux_1_2_x86_64.whl
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Release files / nlpql-0.2.1-cp315-cp315-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl

Download URL	nlpql-0.2.1-cp315-cp315-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl
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Release files / nlpql-0.2.1-cp315-cp315-macosx_15_0_arm64.whl

Download URL	nlpql-0.2.1-cp315-cp315-macosx_15_0_arm64.whl
Size	877.5 kB
Tags	CPython 3.15 macOS 15.0+ ARM64
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Publishing repository: github.com/eggzec/nlpql
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Release files / nlpql-0.2.1-cp314-cp314t-win_amd64.whl

Download URL	nlpql-0.2.1-cp314-cp314t-win_amd64.whl
Size	366.0 kB
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Upload date	Aug 19, 2026
Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/7.0.0 CPython/3.13.14`

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Identity

Publishing platform: GitHub Actions
Publishing repository: github.com/eggzec/nlpql
Publishing commit: github.com/eggzec/nlpql/tree/ff1f4425c10d709cde345970725c208763f1320a

Workflow

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Artifact

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Release files / nlpql-0.2.1-cp314-cp314t-musllinux_1_2_x86_64.whl

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Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/7.0.0 CPython/3.13.14`

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Identity

Publishing platform: GitHub Actions
Publishing repository: github.com/eggzec/nlpql
Publishing commit: github.com/eggzec/nlpql/tree/ff1f4425c10d709cde345970725c208763f1320a

Workflow

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Artifact

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Release files / nlpql-0.2.1-cp314-cp314t-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl

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Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/7.0.0 CPython/3.13.14`

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Identity

Publishing platform: GitHub Actions
Publishing repository: github.com/eggzec/nlpql
Publishing commit: github.com/eggzec/nlpql/tree/ff1f4425c10d709cde345970725c208763f1320a

Workflow

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Artifact

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Release files / nlpql-0.2.1-cp314-cp314t-macosx_15_0_arm64.whl

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Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/7.0.0 CPython/3.13.14`

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Publishing platform: GitHub Actions
Publishing repository: github.com/eggzec/nlpql
Publishing commit: github.com/eggzec/nlpql/tree/ff1f4425c10d709cde345970725c208763f1320a

Workflow

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Artifact

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Release files / nlpql-0.2.1-cp314-cp314-win_amd64.whl

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Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/7.0.0 CPython/3.13.14`

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Identity

Publishing platform: GitHub Actions
Publishing repository: github.com/eggzec/nlpql
Publishing commit: github.com/eggzec/nlpql/tree/ff1f4425c10d709cde345970725c208763f1320a

Workflow

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Artifact

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Release files / nlpql-0.2.1-cp314-cp314-musllinux_1_2_x86_64.whl

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Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/7.0.0 CPython/3.13.14`

Provenance

Identity

Publishing platform: GitHub Actions
Publishing repository: github.com/eggzec/nlpql
Publishing commit: github.com/eggzec/nlpql/tree/ff1f4425c10d709cde345970725c208763f1320a

Workflow

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Artifact

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Release files / nlpql-0.2.1-cp314-cp314-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl

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Upload date	Aug 19, 2026
Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/7.0.0 CPython/3.13.14`

Provenance

Identity

Publishing platform: GitHub Actions
Publishing repository: github.com/eggzec/nlpql
Publishing commit: github.com/eggzec/nlpql/tree/ff1f4425c10d709cde345970725c208763f1320a

Workflow

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Artifact

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Release files / nlpql-0.2.1-cp314-cp314-macosx_15_0_arm64.whl

Download URL	nlpql-0.2.1-cp314-cp314-macosx_15_0_arm64.whl
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Upload date	Aug 19, 2026
Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/7.0.0 CPython/3.13.14`

Provenance

Identity

Publishing platform: GitHub Actions
Publishing repository: github.com/eggzec/nlpql
Publishing commit: github.com/eggzec/nlpql/tree/ff1f4425c10d709cde345970725c208763f1320a

Workflow

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Artifact

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Release files / nlpql-0.2.1-cp313-cp313-win_amd64.whl

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Size	357.5 kB
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Upload date	Aug 19, 2026
Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/7.0.0 CPython/3.13.14`

Provenance

Identity

Publishing platform: GitHub Actions
Publishing repository: github.com/eggzec/nlpql
Publishing commit: github.com/eggzec/nlpql/tree/ff1f4425c10d709cde345970725c208763f1320a

Workflow

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Artifact

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Release files / nlpql-0.2.1-cp313-cp313-musllinux_1_2_x86_64.whl

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Upload date	Aug 19, 2026
Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/7.0.0 CPython/3.13.14`

Provenance

Identity

Publishing platform: GitHub Actions
Publishing repository: github.com/eggzec/nlpql
Publishing commit: github.com/eggzec/nlpql/tree/ff1f4425c10d709cde345970725c208763f1320a

Workflow

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Artifact

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Release files / nlpql-0.2.1-cp313-cp313-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl

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Upload date	Aug 19, 2026
Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/7.0.0 CPython/3.13.14`

Provenance

Identity

Publishing platform: GitHub Actions
Publishing repository: github.com/eggzec/nlpql
Publishing commit: github.com/eggzec/nlpql/tree/ff1f4425c10d709cde345970725c208763f1320a

Workflow

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Artifact

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Release files / nlpql-0.2.1-cp313-cp313-macosx_15_0_arm64.whl

Download URL	nlpql-0.2.1-cp313-cp313-macosx_15_0_arm64.whl
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Upload date	Aug 19, 2026
Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/7.0.0 CPython/3.13.14`

Provenance

Identity

Publishing platform: GitHub Actions
Publishing repository: github.com/eggzec/nlpql
Publishing commit: github.com/eggzec/nlpql/tree/ff1f4425c10d709cde345970725c208763f1320a

Workflow

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Artifact

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Release files / nlpql-0.2.1-cp312-cp312-win_amd64.whl

Download URL	nlpql-0.2.1-cp312-cp312-win_amd64.whl
Size	357.5 kB
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Upload date	Aug 19, 2026
Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/7.0.0 CPython/3.13.14`

Provenance

Identity

Publishing platform: GitHub Actions
Publishing repository: github.com/eggzec/nlpql
Publishing commit: github.com/eggzec/nlpql/tree/ff1f4425c10d709cde345970725c208763f1320a

Workflow

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Artifact

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Release files / nlpql-0.2.1-cp312-cp312-musllinux_1_2_x86_64.whl

Download URL	nlpql-0.2.1-cp312-cp312-musllinux_1_2_x86_64.whl
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Upload date	Aug 19, 2026
Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/7.0.0 CPython/3.13.14`

Provenance

Identity

Publishing platform: GitHub Actions
Publishing repository: github.com/eggzec/nlpql
Publishing commit: github.com/eggzec/nlpql/tree/ff1f4425c10d709cde345970725c208763f1320a

Workflow

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Artifact

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Release files / nlpql-0.2.1-cp312-cp312-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl

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Upload date	Aug 19, 2026
Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/7.0.0 CPython/3.13.14`

Provenance

Identity

Publishing platform: GitHub Actions
Publishing repository: github.com/eggzec/nlpql
Publishing commit: github.com/eggzec/nlpql/tree/ff1f4425c10d709cde345970725c208763f1320a

Workflow

Publishing configuration: github.com/eggzec/nlpql/blob/ff1f4425c10d709cde345970725c208763f1320a/.github/workflows/release-pypi.yml
Publishing logs: github.com/eggzec/nlpql/actions/runs/32241050290/attempts/1

Artifact

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SHA-256 checksum: 92214923b656ca914b74b0006e4922e03433fc7f0a738e6e689ff7f83daba0e1 Verifying attestations

Release files / nlpql-0.2.1-cp312-cp312-macosx_15_0_arm64.whl

Download URL	nlpql-0.2.1-cp312-cp312-macosx_15_0_arm64.whl
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Upload date	Aug 19, 2026
Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/7.0.0 CPython/3.13.14`

Provenance

Identity

Publishing platform: GitHub Actions
Publishing repository: github.com/eggzec/nlpql
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Release files / nlpql-0.2.1-cp311-cp311-win_amd64.whl

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Release files / nlpql-0.2.1-cp311-cp311-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl

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Release files / nlpql-0.2.1-cp311-cp311-macosx_15_0_arm64.whl

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Size	357.5 kB
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Release files / nlpql-0.2.1-cp310-cp310-musllinux_1_2_x86_64.whl

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Release files / nlpql-0.2.1-cp310-cp310-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl

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Release files / nlpql-0.2.1-cp310-cp310-macosx_15_0_arm64.whl

Download URL	nlpql-0.2.1-cp310-cp310-macosx_15_0_arm64.whl
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Publishing commit: github.com/eggzec/nlpql/tree/ff1f4425c10d709cde345970725c208763f1320a

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Release history Release notifications | RSS feed

This release

0.2.1 This release

Aug 19, 2026 32 release files

0.2.0

Aug 16, 2026 32 release files

0.1.0

Aug 15, 2026 32 release files

nlpql 0.2.1

NLPQL

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Nonlinear programming

Data fitting and multicriteria optimization

Quadratic programming

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