Argonne National Laboratory

Upcoming Events

Set-Valued Steepest Descent for Binary Topology and Control Optimization

Series 
LANS Informal Seminar
Presenter 
Mirko Hahn (MCS)
May 9, 2018 10:30AM to 11:30AM
Location 
Building 240, Room 1404-1405
Type 
Seminar

Abstract: PDE- and ODE-constrained optimization problems with integer-valued control functions are often computationally intractable using the first discretize, then optimize approach. This is mainly because computational complexity generally increases exponentially with the number of integer variables, which increases quickly as control meshes are refined.

We discuss a method that avoids these issues for a class of problems with a single binary-valued control function by reformulating the original problem as an optimization problem over the sigma-algebra of Lebesgue-measurable sets. By reformulating the problem in terms of set-valued variables, we can transfer much of the theory of continuous nonlinear programming to mixed-integer problems, which we demonstrate by developing a trust-region steepest descent algorithm.

In addition, we address issues of precision and convergence, as well as possible extensions and theoretical limitations of our approach.

This seminar will be streamed.