Null Space Optimizer¶

nullspace_optimizer is a Python package implementing the null space algorithm for nonlinear constrained optimization. It has been developped 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

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

Null space gradient flow trajectories — Optimization trajectories produced by the Null Space Optimizer for an inequality constrained optimization problem with different initialization.¶

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..

bibtex

@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
}

bibtex

@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.