Advanced Optimization Methodologies for Signal Processing and Communication

研究了某些凸锥可以用正半定矩阵锥的线性像表示或近似的条件。这些条件是对由鲁棒优化引起的半无限约束进行精确有限重新表述的必要工具。该项目侧重于非负映射锥体及其在鲁棒优化中的应用，分析自适应滤波和鲁棒波束形成的内部点方法，以及设计和分析多用户通信系统以及多输入多输出无线通信信道中解码和检测的有效优化方法。这些理论问题都是由需要开发有效的优化算法来解决信号处理和数字通信系统中的问题所强烈激发的。该项目旨在开发新的计算技术来解决信息和通信技术领域的问题。在过去的三十年里，后者主要依靠传统的数值优化方法，当问题规模变大、数据率很高时，这种方法就会遇到困难。在这个项目中，研究者研究了如何使用最先进的优化技术和计算工具来解决来自信息和通信技术领域的一些众所周知的计算瓶颈。

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.