Oberseminar Numerical Mathematics / Scientific Computing
Alexandre Caboussat
Geneva School of Business Administration, University of Applied Sciences and Arts, Western Switzerland
Numerical Methods for Some Non-Smooth Optimization Problems
Abstract:
Non-smooth constrained optimization problems arise when non-differentiable objective functions or constraints are involved. These problems are strongly related to nonlinear generalized eigenvalues problems or the computation of best constants in Sobolev-type inequalities.
In this talk, we discuss several non-smooth optimization problems, which play important role in the modeling of visco-plastic Bingham flows, the computation of load capacity of elasto-plastic bodies, or the determination of best constants in Sobolev imbeddings. The main goal is to discuss the computation of the global optimum associated with non-smooth operators, typically obtained when the objective function and equality constraints involve $L^1$ or $L^\infty$ norms.
To solve these highly nonlinear problems we combine finite element approximations with augmented Lagrangian based iterative methods. Such iterative approaches allow to decouple differential operators and the nonlinear or non-smooth features of the problems. The numerical results not only justify the methodology used but they also suggest some conjectures of mathematical interest.
This is joint work with Roland Glowinski (Univ. of Houston).
| Date: | 04.02.13 | Time: | 17:00 Uhr | Location: | FU Berlin, Institut für Mathematik, Arnimallee 6, 14195 Berlin. | Room: | 031 Basement |