Set-valued steepest descent for binary topology and control optimization

Event Sponsor: 
Mathmatics and Computer Science Division Seminar - LANS
Start Date: 
May 9 2018 - 10:30am
Building 240/Room 1404-1405
Argonne National Laboratory
Mirko Hahn
Speaker(s) Title: 
Argonne National Laboratory, MCS

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.

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Upcoming Seminars
May 2, 2018, "Computational Design Optimization" Daniel A. Tortorelli, Director for the Center of Design and Optimization, (LLNL); George B. Grim Professor of Mechanical Sciences and Engineering (UIUC)
May 9, 2018, "Set-valued steepest descent for binary topology and control optimization" Mirko Hahn, Predoctoral Appointee (MCS/ANL)
May 16, 2018, "Fast methods for nonsmooth nonconvex problems using variable projection" Aleksandr Aravkin, Assistant Professor (University of Washington Applied Math Department)
May 23, 2018, "TBA"
June 6, 2018, "TBD" Nicola Ferrier, Computer Scientist (MCS/ANL)
June 13, 2018, "TBA" Elise Jennings, Computer Scientist (LCF/ANL)