PDENLPModels.jl

PDENLPModels.jl: An NLPModel API for Optimization Problems with PDE-Constraints - Published in JOSS (2022)

https://github.com/juliasmoothoptimizers/pdenlpmodels.jl

Science Score: 98.0%

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Published in Journal of Open Source Software

Keywords from Contributors

pde krylov linear-systems interpretability meshing fluxes finite-elements standardization gridap numerical-methods

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Repository

A NLPModel API for optimization problems with PDE-constraints

Basic Info

Host: GitHub
Owner: JuliaSmoothOptimizers
License: other
Language: Julia
Default Branch: main
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Size: 5.29 MB

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Created over 5 years ago · Last pushed about 1 year ago

Metadata Files

Readme License Citation

PDENLPModels

| Documentation | CI | Coverage | Release | DOI | |:-----------------:|:------:|:------------:|:-----------:|:-------:| | | | | | |

PDENLPModels specializes the NLPModel API to optimization problems with partial differential equations in the constraints. The package relies on Gridap.jl for the modeling and the computation of the derivatives. Find tutorials for using Gridap here.

We consider optimization problems of the form: Find functions $(y,u): Y \times U \rightarrow ℜⁿ \times ℜⁿ$ and $κ \in ℜⁿ$ satisfying

$$ \begin{equation} \begin{array}{cl} \min{\kappa,y,u} & \int\Omega f(\kappa,y,u) d\Omega \ \text{ s.t. } & y \text{ solution of a } PDE(\kappa,u)=0, \ & lcon \leq c(\kappa,y,u) \leq ucon, \ & lvar \leq (\kappa,y,u) \leq uvar,\ \end{array} \end{equation} $$

We refer to the the repository PDEOptimizationProblems for examples of problems of different types: calculus of variations, optimal control problem, PDE-constrained problems, and mixed PDE-contrained problems with both function and algebraic unknowns.

Installation

] add PDENLPModels The current version of PDENLPModels relies on Gridap v0.15.5.

Example

$$ \begin{equation} \min{y \in H^10,u \in H^1} \frac{1}{2} \int{\Omega} |y(x) - yd(x)|^2dx + \frac{\alpha}{2} \int_{\Omega} |u|^2 \quad \text{ s.t. } -\Delta y = u + h, \text{ for } x \in \Omega, y = 0 \text{ for } x \in \partial \Omega, \end{equation} $$

where $yd(x) = -x1^2$, $h(x) = 1$ and $\alpha = 10^{-2}$.

```julia using Gridap, PDENLPModels

# Definition of the domain n = 100 domain = (-1, 1, -1, 1) partition = (n, n) model = CartesianDiscreteModel(domain, partition)

# Definition of the spaces: valuetype = Float64 reffe = ReferenceFE(lagrangian, valuetype, 2) Xpde = TestFESpace(model, reffe; conformity = :H1, dirichlet_tags = "boundary") y0(x) = 0.0 Ypde = TrialFESpace(Xpde, y0)

reffecon = ReferenceFE(lagrangian, valuetype, 1) Xcon = TestFESpace(model, reffecon; conformity = :H1) Ycon = TrialFESpace(Xcon)

# Integration machinery trian = Triangulation(model) degree = 1 dΩ = Measure(trian, degree)

# Objective function: yd(x) = -x[1]^2 α = 1e-2 function f(y, u) ∫(0.5 * (yd - y) * (yd - y) + 0.5 * α * u * u) * dΩ end

# Definition of the constraint operator ω = π - 1 / 8 h(x) = -sin(ω * x[1]) * sin(ω * x[2]) function res(y, u, v) ∫(∇(v) ⊙ ∇(y) - v * u - v * h) * dΩ end

# initial guess npde = numfreedofs(Ypde) ncon = numfreedofs(Ycon) xin = zeros(npde + ncon)

nlp = GridapPDENLPModel(xin, f, trian, Ypde, Ycon, Xpde, Xcon, res, name = "Control elastic membrane") ```

References

Migot, T., Orban D., & Siqueira A. S. PDENLPModels.jl: A NLPModel API for optimization problems with PDE-constraints Journal of Open Source Software 7(80), 4736 (2022). 10.21105/joss.04736

Badia, S., & Verdugo, F. Gridap: An extensible Finite Element toolbox in Julia. Journal of Open Source Software, 5(52), 2520 (2020). 10.21105/joss.02520

How to Cite

If you use PDENLPModels.jl in your work, please cite using the format given in CITATION.cff.

Bug reports and discussions

If you think you found a bug, feel free to open an issue. Focused suggestions and requests can also be opened as issues. Before opening a pull request, start an issue or a discussion on the topic, please.

If you want to ask a question not suited for a bug report, feel free to start a discussion here. This forum is for general discussion about this repository and the JuliaSmoothOptimizers, so questions about any of our packages are welcome.

Owner

Name: JuliaSmoothOptimizers
Login: JuliaSmoothOptimizers
Kind: organization
Location: DOI: 10.5281/zenodo.2655082

Website: https://juliasmoothoptimizers.github.io
Repositories: 63
Profile: https://github.com/JuliaSmoothOptimizers

Infrastructure and Solvers for Continuous Optimization in Julia

JOSS Publication

PDENLPModels.jl: An NLPModel API for Optimization Problems with PDE-Constraints

Published

December 16, 2022

DOI

10.21105/joss.04736

Volume 7, Issue 80, Page 4736

Authors

Tangi Migot

GERAD and Department of Mathematics and Industrial Engineering, Polytechnique Montréal, QC, Canada.

Dominique Orban

GERAD and Department of Mathematics and Industrial Engineering, Polytechnique Montréal, QC, Canada.

Abel Soares Siqueira

Netherlands eScience Center, Amsterdam, NL

Editor

Mehmet Hakan Satman

Citation (CITATION.cff)

# This CITATION.cff file was generated with cffinit.
# Visit https://bit.ly/cffinit to generate yours today!

cff-version: 1.2.0
title: >-
  PDENLPModels.jl: A NLPModel API for optimization problems with PDE-constraints
message: >-
  If you use this software, please cite it using the
  metadata from this file.
type: software
authors:
  - given-names: Tangi
    family-names: Migot
    email: tangi.migot@gmail.com
    affiliation: >-
      GERAD and Department of Mathematics and
      Industrial Engineering, Polytechnique Montréal,
      QC, Canada.
    orcid: 'https://orcid.org/0000-0001-7729-2513'
  - given-names: Dominique
    family-names: Orban
    email: dominique.orban@gerad.ca
    orcid: 'https://orcid.org/0000-0002-8017-7687'
    affiliation: >-
      GERAD and Department of Mathematics and
      Industrial Engineering, Polytechnique Montréal,
      QC, Canada
  - affiliation: 'Netherlands eScience Center, Amsterdam, NL'
    orcid: 'https://orcid.org/0000-0003-4451-281X'
    email: abel.s.siqueira@gmail.com
    given-names: Abel
    family-names: Soares Siqueira
  - given-names: contributors
identifiers:
  - description: Zenodo archive
    type: doi
    value: 10.5281/zenodo.5056628
preferred-citation:
  type: article
  authors:
  - family-names: "Migot"
    given-names: "Tangi"
    orcid: "https://orcid.org/0000-0001-7729-2513"
  - family-names: "Orban"
    given-names: "Dominique"
    orcid: "https://orcid.org/0000-0002-8017-7687"
  - family-names: "Soares Siqueira"
    given-names: "Abel"
    orcid: "https://orcid.org/0000-0003-4451-281X"
  doi: "10.21105/joss.04736"
  journal: "The Journal of Open Source Software"
  month: 12
  start: 4736 # First page number
  title: "PDENLPModels.jl: A NLPModel API for optimization problems with PDE-constraints"
  issue: 80
  volume: 7
  year: 2022
keywords:
  - Nonlinear Optimization
  - Julia
  - Nonlinear Programming
  - PDE-constrained Optimization
  - Optimal Control
license: MPL-2.0
repository-code: >-
  https://github.com/JuliaSmoothOptimizers/PDENLPModels.jl

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juliahub.com: PDENLPModels

A NLPModel API for optimization problems with PDE-constraints

Documentation: https://docs.juliahub.com/General/PDENLPModels/stable/
License: MPL-2.0
Latest release: 0.3.5
published almost 2 years ago

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PDENLPModels.jl

Science Score: 98.0%

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PDENLPModels

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