Seminar Details
2024-11-12 (14h) : Null space gradient flows and applications to topology optimization
At Euler building (room A.002)
Organized by Mathematical Engineering
Speaker :
Florian Feppon ((KU Leuven))
Abstract :
In this seminar, I will present the "Null Space Optimizer" [1,2] which is an algorithm developed for solving nonlinear optimization programs with differentiable equality and inequality constraints.
The main principle of the algorithm is to discretize a dynamical system whose trajectories simultaneously and gradually correct the violation of the constraints while minimizing the objective function.
As a result, one of its appealing aspects comes from its relative independence to the need for tuning unintuitive algorithm parameters. I will show some applications of the algorithm to topology optimization
and discuss a recent extension that enables the optimizer to solve problems with both a large design spaces and many constraints with sparse jacobian matrix.
[1] Feppon, F., Allaire, G. and Dapogny, C. Null space gradient flows for constrained optimization with applications to shape optimization (2020). ESAIM: COCV, 26 9.
[2] 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.