Mathematics and Statistics Colloquium (Oct 17)
Speaker: Dr. Sven Leyffer, https://www.anl.gov/profile/sven-leyffer
Time: October 17, 4-5pm
Location: TBD
Title: Topological Design Problems and Integer Optimization
Abstract: Topological design problems arise in many important engineering and scientific applications, such additive manufacturing and the design of cloaking devices. We formulate these problems as massive mixed-integer PDE-constrained optimization (MIPDECO) problems. We show that despite their seemingly hopeless complexity, MIPDECOs can be solved efficiently (at a cost comparable to a single continuous PDE-constrained optimization solve). We discuss two classes of methods: rounding techniques that are shown to be asymptotically optimal, and trust-region techniques that converge under mesh refinement. We illustrate these solution techniques with examples from topology optimization.
Speaker: Dr. Sven Leyffer, https://www.anl.gov/profile/sven-leyffer
Time: October 17, 4-5pm
Location: TBD
Title: Topological Design Problems and Integer Optimization
Abstract: Topological design problems arise in many important engineering and scientific applications, such additive manufacturing and the design of cloaking devices. We formulate these problems as massive mixed-integer PDE-constrained optimization (MIPDECO) problems. We show that despite their seemingly hopeless complexity, MIPDECOs can be solved efficiently (at a cost comparable to a single continuous PDE-constrained optimization solve). We discuss two classes of methods: rounding techniques that are shown to be asymptotically optimal, and trust-region techniques that converge under mesh refinement. We illustrate these solution techniques with examples from topology optimization.