Convex Optimization with Abstract Linear Operators
Abstract:
Domain specific languages (DSLs) for convex optimization, such as CVX and YALMIP and the more recent CVXPY and Convex.jl, are very widely used to rapidly develop, prototype, and solve convex optimization problems of modest size, say, tens of thousands of variables, with linear operators described as sparse matrices. These systems allow a user to specify a convex optimization problem in a very succinct and natural way, and then solve the problem with great reliability, with no algorithm parameter tuning, and a reasonable performance loss compared to a custom solver hand designed and tuned for the problem. In this talk we describe recent progress toward the goal of extending these DSLs to handle large-scale problems that involve linear operators given as abstract operators with fast transforms, such as those arising in image processing and vision, medical imaging, and other application areas. This involves re-thinking the entire stack, from the high-level DSL design down to the low level solvers. (Joint work with Steven Diamond.)
Biography:
Stephen P. Boyd is the Samsung Professor of Engineering, in the Information Systems Laboratory, Electrical Engineering Department, Stanford University. He is a member of the Institute for Mathematical and Computational and Engineering, and holds courtesy appointments in the department of Computer Science and the department of Management Science and Engineering. His current interests include convex programming applications in control, signal processing, and circuit design. He received an AB degree in Mathematics, summa cum laude, from Harvard University in 1980, and a PhD in EECS from U. C. Berkeley in 1985. He holds an honorary PhD from Royal Institute of Technology, Stockholm. He is the author of Linear Controller Design: Limits of Performance (with Craig Barratt, 1991), Linear Matrix Inequalities in System and Control Theory (with L. El Ghaoui, E. Feron, and V. Balakrishnan, 1994), and Convex Optimization (with Lieven Vandenberghe, 2004). He received an ONR Young Investigator Award, a Presidential Young Investigator Award, the 1992 AACC Donald P. Eckman Award, and the 2013 IEEE Technical Field Award in Control Systems. In 2012, he and former student Michael Grant were awarded the Mathematical Optimization Society Beale-Orchard-Hays award for computational optimization. He has received the Perrin Award for Outstanding Undergraduate Teaching in the School of Engineering, and an ASSU Graduate Teaching Award. In 2003, he received the AACC Ragazzini Education award. He is a fellow of the IEEE, a Distinguished Lecturer of the IEEE Control Systems Society, and a member of the National Academy of Engineering.