Convex optimization has emerged as useful tool for applications that include data analysis and model fitting, resource allocation, engineering design, network design and optimization, finance, control and signal processing, and circuit sizing. After an overview of the mathematics, algorithms, and software frameworks for convex optimization, we turn to common themes that arise across applications, such as sparsity and relaxation. We describe recent work on real-time embedded convex optimization, in which small problems are solved repeatedly and reliably in millisecond or microsecond time frames, with growing applications in control and resource allocation.
Stephen P. Boyd is the Samsung Professor of Engineering, and Chair of the Electrical Engineering Department at Stanford University. He holds courtesy appointments in the departments of Computer Science and Management Science and Engineering, and is a member of the Institute for Computational Mathematics and Engineering.
His current interests include convex optimization applications in control, machine learning, signal processing, and finance. 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 honorary doctorates from Royal Institute of Technology (KTH) and Catholic University of Louvain (UCL). He is the author of many papers and several books, including Introduction to Applied Linear Algebra, Convex Optimization, Linear Matrix Inequalities in Systems and Control, and Linear Controller Design: Limits of Performance.
His group has created many open source software packages, including the widely used packages for convex optimization CVX, CVXPY, and Convex.jl. He is a fellow of IEEE, SIAM, and INFORMS, a member of the National Academy of Engineering, a foreign member of the Chinese Academy of Engineering, and a foreign member of the National Academy of Engineering of Korea. (See https://web.stanford.edu/~boyd/)