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

南加州的欧文·S·里德在这项研究中，我们将研究一类凸优化问题(COPS)的分析可行和计算有效的方法。这些问题在许多信息处理应用中经常遇到，特别是在配备多个发射(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联合优化设计和功率控制。本文将研究两种类型的凸优化问题：(1)无约束或有等式约束；(2)有混合等式和不等式约束。传统的Rx波束形成(分集合并)大多属于第一类，而当涉及具有功率控制的联合Tx-Rx优化时，问题往往是复杂的混合约束，并成为第二类。第一类COPS的闭合解在许多情况下是已知的，但很难实时计算，而第二类COPS可能不是解析可解的。

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.