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LANS Informal Seminar: Mirko Hahn
May 9, 2018 @ 10:30 CDT
Seminar Title: Set-valued steepest descent for binary topology and control optimization
Speaker: Mirko Hahn, Predoctoral Appointee, MCS/ANL
Date/Time: 2018-05-09 10:30
Location: Bldg. 240. Rm. 1404-1405
Description:
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 which 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.