Enlsip.jl

Enlsip.jl: A Julia optimization package to solve constrained nonlinear least-squares problems - Published in JOSS (2024)

https://github.com/uncertainlab/enlsip.jl

Science Score: 67.0%

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Repository

Enlsip.jl is the Julia version of a Fortran77 optimization library designed to solve nonlinear least squares problems under general nonlinear constraints.

Basic Info

Host: GitHub
Owner: UncertainLab
License: mit
Language: Julia
Default Branch: main
Size: 395 KB

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Stars: 8
Watchers: 1
Forks: 2
Open Issues: 1
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Created over 2 years ago · Last pushed 11 months ago

Metadata Files

Readme License Citation

Enlsip.jl

Package Enlsip.jl is the Julia version of ENLSIP, an open source algorithm originally written in Fortran77 and designed to solve nonlinear least-squares problems subject to nonlinear constraints. The optimization method implemented in ENLSIP is described in

Per Lindström and Per-Åke Wedin, Gauss Newton based algorithms for constrained nonlinear least squares problems. Technical Report S-901 87, Institute of Information processing, University of Umeå, Sweden, 1988.

The source code of the Fortran77 library is available at https://plato.asu.edu/sub/nonlsq.html.

Problems that can be solved using Enlsip.jl are modeled as follows:

math \begin{aligned} \min_{x \in \mathbb{R}^n} \quad & \dfrac{1}{2} \|r(x)\|^2 \\ \text{s.t.} \quad & c_i(x) = 0, \quad i \in \mathcal{E} \\ & c_i(x) \geq 0, \quad i \in \mathcal{I}, \\ & l_i \leq x_i \leq u_i, \quad i \in \{1,\ldots,n\}, \end{aligned}

where:

the residuals $ri:\mathbb{R}^n\rightarrow\mathbb{R}$ and the constraints $ci:\mathbb{R}^n\rightarrow\mathbb{R}$ are assumed to be $\mathcal{C}^2$ functions;
norm $||\cdot||$ denotes the Euclidean norm;
$l$ and $u$ are respectively vectors of lower and upper bounds.

In the formulation above, bound constraints are written seperately but they are treated as classical inequality constraints in the method implemented in ENLSIP.

How to install

To add Enlsip, use Julia's package manager by typing the following command inside the REPL:

julia using Pkg Pkg.add("Enlsip")

How to Use

Solving a problem with Enlsip is organized in two steps.

First, you need to create a model of your problem with the CnlsModel structure.

Creating a model

An object of type CnlsModel can be created using a constructor, whose arguments are the following:

residuals : function that computes the vector of residuals
nb_parameters : number of variables
nb_residuals : number of residuals
stating_point : initial solution
jacobian_residuals : function that computes the jacobian matrix of the residuals. If not passed as argument, it is computed numericcaly by forward differences
eq_constraints : function that computes the vector of equality constraints
jacobian_eqcons : function that computes the jacobian matrix of the equality constraints. If not passed as argument, it is computed numericcaly by forward differences
nb_eqcons : number of equality constraints
ineq_constraints : function that computes the vector of inequality constraints
jacobian_ineqcons : function that computes the jacobian matrix of the inequality constraints. If not passed as argument, it is computed numericcaly by forward differences
nb_ineqcons : number of inequality constraints
x_low and x_upp : respectively vectors of lower and upper bounds

Solving a model

Then, once your model is instantiated, you can call the solve! function to solve your problem.

Example with problem 65 from Hock Schittkowski collection[^HS80]

```julia

Import Enlsip

using Enlsip

Dimensions of the problem

n = 3 # number of parameters m = 3 # number of residuals

Residuals and jacobian matrix associated

r(x::Vector) = [x[1] - x[2]; (x[1]+x[2]-10.0) / 3.0; x[3]-5.0]

jac_r(x::Vector) = [1. -1. 0; 1/3 1/3 0.; 0. 0. 1.]

Constraints (one nonlinear inequality and box constraints)

c(x::Vector) = [48.0 - x[1]^2-x[2]^2-x[3]^2] jacc(x::Vector) = [ -2x[1] -2x[2] -2x[3]] xl = [-4.5, -4.5, -5.0] x_u = [4.5, 4.5, 5.0]

Starting point

x0 = [-5.0, 5.0, 0.0]

Instantiate a model associated with the problem

hs65model = Enlsip.CnlsModel(r, n, m ;jacobianresiduals=jacr, startingpoint=x0, ineqconstraints = c, jacobianineqcons=jacc, nbineqcons = 1, xlow=xl, xupp=xu)

Call of the `solve!` function

Enlsip.solve!(hs65_model)

Print solution and objective value

println("Algorithm termination status: ", Enlsip.status(hs65model)) println("Optimal solution: ", Enlsip.solution(hs65model)) println("Optimal objective value: ", Enlsip.sumsqresiduals(hs65_model)) ```

[^HS80]: W. Hock and K. Schittkowski. Test Examples for Nonlinear Programming Codes, volume 187 of Lecture Notes in Economics and Mathematical Systems. Springer, second edition, 1980.

Owner

Name: UncertainLab
Login: UncertainLab
Kind: organization

Repositories: 1
Profile: https://github.com/UncertainLab

Citation (CITATION.cff)

cff-version: "1.2.0"
authors:
- family-names: Borie
  given-names: Pierre
  orcid: "https://orcid.org/0009-0000-1043-5057"
- family-names: Marcotte
  given-names: Alain
  orcid: "https://orcid.org/0009-0009-5964-8892"
- family-names: Bastin
  given-names: Fabian
  orcid: "https://orcid.org/0000-0003-1323-6787"
- family-names: Dellacherie
  given-names: Stéphane
  orcid: "https://orcid.org/0009-0005-9043-9328"
doi: 10.5281/zenodo.11206280
message: If you use this software, please cite our article in the
  Journal of Open Source Software.
preferred-citation:
  authors:
  - family-names: Borie
    given-names: Pierre
    orcid: "https://orcid.org/0009-0000-1043-5057"
  - family-names: Marcotte
    given-names: Alain
    orcid: "https://orcid.org/0009-0009-5964-8892"
  - family-names: Bastin
    given-names: Fabian
    orcid: "https://orcid.org/0000-0003-1323-6787"
  - family-names: Dellacherie
    given-names: Stéphane
    orcid: "https://orcid.org/0009-0005-9043-9328"
  date-published: 2024-05-22
  doi: 10.21105/joss.06226
  issn: 2475-9066
  issue: 97
  journal: Journal of Open Source Software
  publisher:
    name: Open Journals
  start: 6226
  title: "Enlsip.jl: A Julia optimization package to solve constrained
    nonlinear least-squares problems"
  type: article
  url: "https://joss.theoj.org/papers/10.21105/joss.06226"
  volume: 9
title: "Enlsip.jl: A Julia optimization package to solve constrained
  nonlinear least-squares problems"

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Total versions: 9

juliahub.com: Enlsip

Enlsip.jl is the Julia version of a Fortran77 optimization library designed to solve nonlinear least squares problems under general nonlinear constraints.

Documentation: https://docs.juliahub.com/General/Enlsip/stable/
License: MIT
Latest release: 0.9.7
published over 1 year ago

Versions: 9
Dependent Packages: 0
Dependent Repositories: 0
Downloads: 1 Total

Rankings

Dependent repos count: 10.2%

Dependent packages count: 37.6%

Average: 42.0%

Forks count: 54.2%

Stargazers count: 66.0%

Last synced: 6 months ago

Enlsip.jl

Science Score: 67.0%

Scientific Fields

Repository

Basic Info

Statistics

Metadata Files

README.md

Enlsip.jl

How to install

How to Use

Creating a model

Solving a model

Example with problem 65 from Hock Schittkowski collection[^HS80]

Import Enlsip

Dimensions of the problem

Residuals and jacobian matrix associated

Constraints (one nonlinear inequality and box constraints)

Starting point

Instantiate a model associated with the problem

Call of the solve! function

Print solution and objective value

Owner

Citation (CITATION.cff)

GitHub Events

Total

Last Year

Committers

All Time

Past Year

Top Committers

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juliahub.com: Enlsip

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Call of the `solve!` function