CIF: Small: A Simple and Unifying Optimization Framework for Signal and Information Processing Problems with Min-Max Structures

Over the past two decades, advances in signal and information processing have been heavily influenced by new developments in optimization. Modern optimization methods, from linear programming to convex optimization, have become indispensable tools to approach problems that arise in a number of core application areas such as compressive sensing, bioinformatics, wireless communication, and data analytics. Meanwhile, the tremendous growth in optimization algorithms for signal processing applications calls for the development of unifying frameworks, which can help simplify our understanding of algorithmic behavior, predict performance, and streamline the design of application-specific algorithms. The framework developed in this project will benefit a wide range of applications well beyond signal processing, including machine learning, data mining and computer vision. The proposed efforts also offer rich and varied opportunities for engaging undergraduate students in cross-disciplinary research, as well as in K12 outreach activities.

This project is focused on designing a framework that deals with a challenging class of block Minimization-Maximization problems, which involves jointly minimizing and maximizing a particular class of structured objective functions. This covers many signal processing applications, old and new, such as min rate utility maximization and robust data analytics. This project will take a bottom-up approach, where starting from a relatively simple formulation, problem-specific features and properties will be gradually built. Rigorous performance analysis will be conducted, and the resulting algorithms will be specialized and evaluated in a number of signal processing applications, including wireless resource allocation in the presence of jammers.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.