TF: Dimension Reduction Approach to Convex Optimization: Theory, Algorithms, and Applications

TF：凸优化的降维方法：理论、算法和应用

• 批准号: 0515358
• 负责人: Irving Reed
• 金额: $ 30万
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-08-01 至 2009-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0515358&HistoricalAwards=false
• 关键词: TF; Dimension; Reduction; Approach; Convex

ABSTRACT0515358Irving S. ReedU of Southern CaliforniaIn this research we will study a methodology for solving a class of convex optimization problems (COPs) in analytically feasible and computationally efficient ways. These problems are frequently encountered in many information processing applications, especially in wireless communication systems equipped with multiple transmit (Tx) and receive (Rx) antennas for beamforming, equalization, joint optimal design of Tx-Rx and power control. Two types of convex optimization will be investigated in this research: (1) un-constrainedor constrained with equalities, and (2) constrained with mixed equalities and inequalities. Most ofconventional beamformings (diversity combining) at Rx fall into the first type, whereas, when joint Tx-Rx optimizations with power control are involved, the problems tend to be complicated with mixed constraints, and become the second type. The closed-form solutions to related COPs of the first type are known in many cases, but difficult to compute in real time, whereas some COPs of the second type may not be analytically solvable.

摘要0515358欧文S.南加州ReedU在这项研究中，我们将研究一种以分析可行且计算高效的方式解决一类凸优化问题（COP）的方法。这些问题在许多信息处理应用中经常遇到，特别是在配备有用于波束成形、均衡、Tx-Rx的联合优化设计和功率控制的多个发射（Tx）和接收（Rx）天线的无线通信系统中。 本研究将探讨两种类型的凸最佳化：（1）无约束或有等式约束的凸最佳化，以及（2）有等式与不等式混合的凸最佳化。传统的接收端波束形成（分集合并）多属于第一类，而当联合Tx-Rx优化与功率控制相结合时，由于混合约束的存在，问题变得复杂，成为第二类。第一类相关COP的封闭形式解在许多情况下是已知的，但难以在真实的时间内计算，而第二类的某些COP可能不是解析可解的。