IE-CS-OPIM Joint Seminar
Prof.Robert Freund Massachusetts Institute of Technology (MIT)
October 17, 2012, Wednesday @ 13:40pm @ FENS G029
“Implementation-Robust Design: Modeling, Theory, and Application to Photonic Crystal Design with Bandgaps”
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.
This is joint work with Abby Men, Joel Saa-Seoane, Ngoc Cuong Nguyen, Jaime Peraire at MIT.
Robert Freund is the Theresa Seley Professor in Management Science at the Sloan School of Management at MIT. He received his B.A. in Mathematics from Princeton University and M.S. and Ph.D. degrees in Operations Research at Stanford University. He has served as Co-Editor of the journal Mathematical Programming and Associate Editor of several optimization and operations research journals. He is the former Co-Director of MIT Operations Research Center, the MIT Program in Computation for Design and Optimization, and the former Chair of the INFORMS Optimization Section. He also recently served a term as Deputy Dean of the Sloan School at MIT. His main research interests are in convex optimization, computational complexity and related computational science, convex geometry, large-scale nonlinear optimization, and related mathematical systems. He received the Longuet-Higgins Prize in computer vision (2007) as well as numerous teaching and education awards at MIT in conjunction with the course and textbook (co-authored with Dimitris Bertsimas) Data, Models, and Decisions: the Fundamentals of Management Science.