Convex Optimization with Abstract Linear Operators
Stephen P. Boyd
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. This is is joint work by Stephen Boyd & Steven Diamond.
Stephen P. Boyd is the Samsung Professor of Engineering, and Professor of Electrical Engineering in the Information Systems Laboratory at Stanford University. He has courtesy appointments in the Department of Management Science and Engineering and the Department of Computer Science, and is member of the Institute for Computational and Mathematical Engineering. His current research focus is on convex optimization applications in control, signal processing, and circuit design.
Professor Boyd 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. In 1985 he joined the faculty of Stanford's Electrical Engineering Department. He has held visiting Professor positions at Katholieke University (Leuven), McGill University (Montreal), Ecole Polytechnique Federale (Lausanne), Tsinghua University (Beijing), Universite Paul Sabatier (Toulouse), Royal Institute of Technology (Stockholm), Kyoto University, Harbin Institute of Technology, NYU, MIT, UC Berkeley, and CUHK-Shenzhen. He holds an honorary doctorate from Royal Institute of Technology (KTH), Stockholm.
Professor Boyd is the author of many research articles and three books: Convex Optimization (with Lieven Vandenberghe, 2004), Linear Matrix Inequalities in System and Control Theory (with L. El Ghaoui, E. Feron, and V. Balakrishnan, 1994), and Linear Controller Design: Limits of Performance (with Craig Barratt, 1991). His group has produced several open source tools, including CVX (with Michael Grant), a widely used parser-solver for convex optimization.
Professor Boyd has received many awards and honors for his research in control systems engineering and optimization, including an ONR Young Investigator Award, a Presidential Young Investigator Award, and the AACC Donald P. Eckman Award, given annually for the greatest contribution to the field of control engineering by someone under the age of 35. In 2013, he received the IEEE Control Systems Award, given for outstanding contributions to control systems engineering, science, or technology. In 2012, Michael Grant and he were given the Mathematical Optimization Society's Beale-Orchard-Hays Award, given every three years for excellence in computational mathematical programming. He is a Fellow of the IEEE and SIAM, a Distinguished Lecturer of the IEEE Control Systems Society, and a member of the National Academy of Engineering. He has been invited to deliver more than 75 plenary and keynote lectures at major conferences in control, optimization, and machine learning.
He currently teaches graduate courses on Linear Dynamical Systems and Convex Optimization, each attracting around 250 students from many departments. From 1988 through 2003 he also taught introductory undergraduate Electrical Engineering courses on Circuits, Signals and Systems, Digital Signal Processing, and Automatic Control, as well an advanced course on Nonlinear Feedback Systems. In 1994 he received the Perrin Award for Outstanding Undergraduate Teaching in the School of Engineering, and in 1991, an ASSU Graduate Teaching Award. In 2003, he received the AACC Ragazzini Education award, for contributions to control education, with citation: "For excellence in classroom teaching, textbook and monograph preparation, and undergraduate and graduate mentoring of students in the area of systems, control, and optimization."
His website, which makes available past papers, books, software, lecture notes, and selected lecture videos, is visited more than 1.6 million times per year, not counting accesses to iTunes U, YouTube, Stanford Engineering Everywhere, or MIT Open Course Ware, each of which include courses developed and delivered by Boyd.
At Stanford he has served as director of the Information Systems Laboratory (for ten years), chair of the (university wide) Library Committee, chair of the David Packard EE Building Planning & Design Committee, and as a member of the (university wide) Advisory Board.