Null Space Optimizer

nullspace_optimizer is a Python package implementing the null space algorithm for nonlinear constrained optimization. It has been developed in the context of topology optimization problems with the level-set and the density method, but it can in principle be used for solving arbitrary smooth nonlinear equality and inequality constrained optimization problems of the form

\begin{aligned}
\begin{aligned}
    \min_{x\in \mathcal{X}}&  \quad J(x)\\
    \textrm{s.t.} & \left\{\begin{aligned}
 g_i(x)&=0, \text{ for all } 1\leqslant i\leqslant p,\\
 h_j(x)  &\leqslant  0, \text{ for all }1\leqslant j \leqslant q,\\ 
        \end{aligned}\right.
\end{aligned}
\end{aligned}   

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Official documentation

Official documentation

Contribute and support

• Issue tracker: https://gitlab.com/florian.feppon/null-space-optimizer/-/issues
• Source code: https://gitlab.com/florian.feppon/null-space-optimizer

If I am not responding on the issue tracker, feel free to send me an email to florian.feppon[at]kuleuven.be

Citation

Please cite either of the following references when using this source:

Feppon F., Allaire G. and Dapogny C. Null space gradient flows for constrained optimization with applications to shape optimization. 2020. ESAIM: COCV, 26 90 doi:10.1051/cocv/2020015

Feppon F. Density based topology optimization with the Null Space Optimizer: a tutorial and a comparison (2024).
Structural and Multidisciplinary Optimization, 67(4), 1-34.

@article{feppon2020optim,
   author = {{Feppon, F.} and {Allaire, G.} and {Dapogny, C.}},
   doi = {10.1051/cocv/2020015},
   journal = {ESAIM: COCV},
   pages = {90},
   title = {Null space gradient flows for constrained optimization with applications to shape optimization},
   url = {https://doi.org/10.1051/cocv/2020015},
   volume = 26,
   year = 2020
}

@article{Feppon2024density,
  title     = "Density-based topology optimization with the Null Space Optimizer: a tutorial and a comparison",
  author    = "Feppon, Florian",
  journal   = "Structural and Multidisciplinary Optimization",
  publisher = "Springer",
  volume    =  67,
  number    =  1,
  pages     = "1--34",
  month     =  jan,
  year      =  2024
}

Licence

The Null Space Optimizer is a free software distributed under the terms of the GNU General Public Licence GPL3.