TITLE:  Fabrication-Adaptive Optimization and Its Application to Photonic Crystal Design

SPEAKER: Robert M. Freund

ABSTRACT:

It is often the case that computed solutions of many optimization problems cannot be implemented directly (irrespective of data accuracy) due to either (i) technological limitations (physical tolerances of machines or processes), (ii) the deliberate simplification of a model to keep it tractable (ignoring certain types of constraints that pose computational difficulties), and/or (iii) human factors (getting people to "do" x). Motivated by these observations, we present a modeling paradigm called "fabrication-adaptive optimization" for treating issues of implementation/fabrication, develop computationally-focused theory and algorithms, and produce computational results for incorporating considerations of implementation/fabrication into constrained optimization problems that arise in application settings. The proposed fabrication-adaptive optimization framework stems from the robust regularization of a function (Lewis 2002). We show how to do computation with fabrication-adaptive optimization in spite of challenges of non-convexity, and we apply our methodology to compute fabricable designs of two-dimensional photonic crystals with a variety of prescribed features. This is joint work with Abby Men, Jaime Peraire, Joel Saa-Seoane, and Ngoc C. Nguyen.