Over the past two decades there have been significant advances in the field of optimization. In particular, convex optimization has emerged as a powerful signal processing tool, and the variety of applications continues to grow rapidly. This book, written by a team of leading experts, sets out the theoretical underpinnings of the subject and provides tutorials on a wide range of convex optimization applications. Emphasis throughout is on cutting-edge research and on formulating problems in convex form, making this an ideal textbook for advanced graduate courses and a useful self-study guide. Topics covered range from automatic code generation, graphical models, and gradient-based algorithms for signal recovery, to semidefinite programming (SDP) relaxation and radar waveform design via SDP. It also includes blind source separation for image processing, robust broadband beamforming, distributed multi-agent optimization for networked systems, cognitive radio systems via game theory, and the variational inequality approach for Nash equilibrium solutions.

Table of Contents

1 Automatic code generation for real-time convex optimization

2 Gradient-based algorithms with applications to signal-recovery problems

3 Graphical models of autoregressive processes

4 SDP relaxation of homogeneous quadratic optimization: approximation bounds and applications

5 Probabilistic analysis of semidefinite relaxation detectors for multiple-input, multiple-output systems

6 Semidefinite programming, matrix decomposition, and radar code design

7 Convex analysis for non-negative blind source separation with application in imaging

8 Optimization techniques in modern sampling theory

9 Robust broadband adaptive beamforming using convex optimization

10 Cooperative distributed multi-agent optimization

11 Competitive optimization of cognitive radio MI MO systems via game theory

12 Nash equilibria: the variational approach

About the Authors

Daniel P. Palomar is an Assistant Professor in the Department of Electronic and Computer Engineering at Hong Kong University of Science and Technology. He received his Ph.D. from the Technical University of Catalonia (UPC), Spain, in 2003 and has since received numerous awards including the Best Doctoral Thesis in Advanced Mobile Communications by the Vodafone Foundation and COIT (2004). His current research interests include applications of convex optimization theory, game theory, and variational inequality theory to signal processing and communications.

Yonina C. Eldar is a Professor in the Department of Engineering at Technion, Israel University of Technology, and is also a Research Affiliate with the Research Laboratory of Electronics at MIT. She received her Ph.D. from the Massachusetts Institute of Technology (MIT) in 2001. She has received many awards, including, in 2008, the Hershel Rich Innovation Award, the Award for Women with Distinguished Contributions and the Muriel & David Jacknow Award for Excellence in Teaching.