Real-Time Convex Optimization . . . -- Recent advances that make it easier to design and implement algorithms

1053-5888/10/$26.00©2010IEEE C onvex optimization has been used in signal processing for a long time to choose coefficients for use in fast (linear) algorithms, such as in filter or array design; more recently, it has been used to carry out (nonlinear) processing on the signal itself. Examples of the latter case include total variation denoising, compressed sensing, fault detection, and image classification. In both scenarios, the optimization is carried out on time scales of seconds or minutes and without strict time constraints. Convex optimization has traditionally been considered computationally expensive, so its use has been limited to applications where plenty of time is available. Such restrictions are no longer justified. The combination of dramatically increased computing power, modern algorithms, and new coding approaches has delivered an enormous speed increase, which makes it possible to solve modest-sized convex optimization problems on microsecond or millisecond time scales and with strict deadlines. This enables real-time convex optimization in signal processing.