WC-06: Applications of Optimization I
Stream: Applications of Optimization
Room: Moreau
Chair(s): Michal Kocvara

Topological optimization of porous architectural materials using a multiphysics homogenization method
Godfred AGYEKUM OHENEBA, Laurent Cangemi, François JOUVE
We will present a topological optimization method based on a homogenized formulation of poroelastic type, of a fluid mass transfer problem within a material with periodically controlled microstructure.The optimization consists in minimizing an energy-type objective function, whose physical properties are correlated with a density of matter and with a microstructure at any point of the domain.Examples of optimized design results will be presented.

A Primal-Dual Augmented Lagrangian Algorithm for SDPs in truss topology design
Arefeh Kavand
In this talk, we focus on the augmented Lagrangian framework based on the PENNON algorithm. We suggest a primal-dual approach with a number of useful modifications, for solving large SDP problems with low-rank solutions. For this, we rephrase Newton systems in the PENNON algorithm by primal-dual systems which are then solved approximately by the preconditioned conjugate gradient method using newly designed preconditioners. The efficiency of the algorithm is demonstrated by numerical experiments for truss topology optimization problems with growing dimension.

An Interior-Point Method for Low-Rank Semidefinite Programming with Application to Truss Topology Design
Soodeh Habibi, Michal Kocvara
General algorithms and software for semidefinite optimization are unsuitable to solve very large dimensional problems. In this talk, we focus on SDP problems with low-rank solutions. Within a standard framework of an interior-point method, we solve the linear systems by a preconditioned conjugate gradient method. We present a new preconditioner tailored to the low-rank structure of the solution. We solve large to very large-scale SDP problems from structural optimization with either rank-one or approximate low-rank solutions. In both cases, our Matlab code outperforms available SDP software.