In recent years there have been major advances in the algorithms and software for convex optimization. These research advances are beginning to find exciting applications in digital signal processing and communications, giving powerful new modeling and computational tools to solve previously considered intractable problems.

This tutorial will begin with a basic review of some of the most useful concepts and algorithms in convex optimizations including the interior point algorithms for linear programming, Second Order Cone programming and Semidefinite Programming (SDP). We will consider numerous examples of applications including pulse shaping filter design, robust beamforming, data fusion, channel equalization, transceiver design for multi-access communication, and capacity maximizing precoder design for multi-user communication.

Throughout the tutorial, we will concentrate on how to recognize and exploit convexity (sometimes hidden) in various engineering formulations. In addition, an overview of the state-of-the-art software tools will be provided. The aim of this tutorial is to give attendees the background required to use the modern convex optimization methods in their own research or engineering work.