level-set method – Optimization Online

A level-set-based topology optimization strategy using radial basis functions and a Hilbertian velocity extension

Published: 2022/04/12, Updated: 2022/06/15

Mechanical Engineering, Multidisciplinary Design Optimization, Optimization of Systems modeled by PDEs Hilbertian velocity extension, level-set method, Radial basis function, Shape derivatives, topology optimization

This work addresses the structural compliance minimization problem through a level-set-based strategy that rests upon radial basis functions with compact support combined with Hilbertian velocity extensions. A consistent augmented Lagrangian scheme is adopted to handle the volume constraint. The linear elasticity model and the variational problem associated with the computation of the velocity field are … Read more

On efficiently solving the subproblems of a level-set method for fused lasso problems

Published: 2017/06/28

Xudong Li

Defeng Sun

Kim-Chuan Toh

Convex and Nonsmooth Optimization convex composite programming, fused lasso, generalized jacobian, level-set method, semismooth newton method

In applying the level-set method developed in [Van den Berg and Friedlander, SIAM J. on Scientific Computing, 31 (2008), pp.~890–912 and SIAM J. on Optimization, 21 (2011), pp.~1201–1229] to solve the fused lasso problems, one needs to solve a sequence of regularized least squares subproblems. In order to make the level-set method practical, we develop … Read more