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0515358Irving S. reedu of Southern Californiain这项研究将研究一种方法，用于在分析可行和计算有效的方法中解决一类凸优化问题（COP）。这些问题经常在许多信息处理应用中遇到，尤其是在配备多个传输（TX）和接收（RX）天线的无线通信系统中，用于波束形成，均衡，TX-RX的关节最佳设计和功率控制。 在这项研究中将研究两种类型的凸优化：（1）相等性的无约束性约束，（2）以混合的平等性和不等式约束。 Rx的大多数范围的光束形成（多样性组合）都属于第一种类型，而当涉及功率控制的关节TX-RX优化时，问题往往会因混合约束而变得复杂，并成为第二类。在许多情况下，对第一种类型的COP的封闭形式解决方案是已知的，但是很难实时计算，而第二类的某些COP可能无法在分析上解决。