Advanced Optimization Methodologies for Signal Processing and Communication

University Of Minnesota-Twin Cities, Minneapolis MN

Investigators

Abstract

Luo The imvestigator studies conditions under which certain convex cones can be represented or approximated by linear images of the positive semidefinite matrix cone. These conditions are the essential tools for the exact finite reformulation of semi-infinite constraints arising from robust optimization. The project focusses on cones of nonnegative mappings and applications to robust optimization, analysis of interior point methods for adaptive filtering and robust beamforming, and efficient optimization methods for the design and analysis of multi-user communication systems and for decoding and detection in multi-input-multi-output wireless communication channels. The theoretical issues are all strongly motivated by the need to develop efficient optimization algorithms for problems in signal processing and digital communication systems. The project aims at developing new computational techniques to solve problems in the information and communication technology area. The latter area has, over the last thirty years, been relying mostly on traditional numerical optimization methods, which can run into difficulty when the problem size becomes large or when data rate is high. In this project, the investigator studies ways to use state-of-the-art optimization techniques and computational tools to resolve some well-known computational bottlenecks from the information and communication technology area.