Advanced Optimization Methodologies for Signal Processing and Communication

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Luo The imvestigator studies conditions under which certainconvex cones can be represented or approximated by linear imagesof the positive semidefinite matrix cone. These conditions arethe essential tools for the exact finite reformulation ofsemi-infinite constraints arising from robust optimization. Theproject focusses on cones of nonnegative mappings andapplications to robust optimization, analysis of interior pointmethods for adaptive filtering and robust beamforming, andefficient optimization methods for the design and analysis ofmulti-user communication systems and for decoding and detectionin multi-input-multi-output wireless communication channels. Thetheoretical issues are all strongly motivated by the need todevelop efficient optimization algorithms for problems in signalprocessing and digital communication systems. The project aims at developing new computational techniquesto solve problems in the information and communication technologyarea. The latter area has, over the last thirty years, beenrelying mostly on traditional numerical optimization methods,which can run into difficulty when the problem size becomes largeor when data rate is high. In this project, the investigatorstudies ways to use state-of-the-art optimization techniques andcomputational tools to resolve some well-known computationalbottlenecks from the information and communication technologyarea.