Monday, 15:45 - 16:10 h, Room: H 2036

 

Robert Freund
Implementation-robust design: Modeling, theory, and application to photonic crystal design with bandgaps

Coauthors: Han Men, Ngoc Cuong Nguyen, Jaime Peraire, Joel Saa-Seoane

 

Abstract:
We present a new theory for incorporating considerations of implementation into optimization models quite generally. Computed solutions of many optimization problems cannot be implemented directly due to (i) the deliberate simplification of the model, and/or (ii) human factors and technological reasons. We propose a new alternative paradigm for treating issues of implementation that we call "implementation robustness.'' This paradigm is applied to the setting of optimizing the fabricable design of photonic crystals with large band-gaps. Such designs enable a wide variety of prescribed interaction with and control of mechanical and electromagnetic waves. We present and use an algorithm based on convex conic optimization to design fabricable two-dimensional photonic crystals with large absolute band gaps. Our modeling methodology yields a series of finite-dimensional eigenvalue optimization problems that are large-scale and non-convex, with low regularity and non-differentiable objective. By restricting to appropriate eigen-subspaces, we reduce the problem to a sequence of small-scale SDPs for which modern SDP solvers are successfully applied.

 

Talk 2 of the contributed session Mon.3.H 2036
"Semidefinite programming applications" [...]
Cluster 4
"Conic programming" [...]

 

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