DFMethods

Derivative-free projection methods for constrained nonlinear equations, integrated with NonlinearSolve.jl.

Solve

$$\text{Find } u^* \in X \subset \mathbb{R}^n \text{ such that } F(u^*) = 0,$$

where $X$ is closed convex and $F$ is continuous and (pseudo-)monotone. No derivatives required.

Install

] add DFMethods

Full installation options (registry, REPL, unreleased-from-GitHub) are on the docs home page.

Documentation

Full documentation: https://mmogib.github.io/DFMethods.jl/stable/.

• Quickstart — runnable examples for unconstrained, box, and convex-set problems
• Algorithm — the outer-iteration structure and pluggable components
• Constraint Sets — built-in feasibility sets and ConstrainedNonlinearProblem
• Extending — define your own search direction, line search, iterate update, …
• Comparisons — DFMethods.jl vs related Julia packages
• API Reference

Citation

If you use DFMethods.jl in research, please cite it via the Zenodo DOI:

@software{Alshahrani_DFMethods_2026,
  author    = {Alshahrani, Mohammed},
  title     = {{DFMethods.jl: A configurable framework for derivative-free projection methods for constrained nonlinear equations}},
  month     = jun,
  year      = 2026,
  publisher = {Zenodo},
  version   = {v0.3.3},
  doi       = {10.5281/zenodo.20350220},
  url       = {https://doi.org/10.5281/zenodo.20350220}
}

The machine-readable equivalent is in CITATION.cff — GitHub's Cite this repository button uses this file. Each tagged release also has a version-specific Zenodo DOI; see the GitHub Releases page or the Zenodo record.

If you build on a specific algorithmic component, please additionally cite the originating source — each component's docstring names it with a DOI link.

License

MIT