On implementation of a self-dual embedding method for convex programming.

by Cheng Tak Wai, Johnny.Thesis (M.Phil.)--Chinese University of Hong Kong, 2003.Includes bibliographical references (leaves 59-62).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.1Chapter 2 --- Background --- p.7Chapter 2.1 --- Self-dual embedding --- p.7Chapter 2.2 --- Conic optimization --- p.8Chapter 2.3 --- Self-dual embedded conic optimization --- p.9Chapter 2.4 --- Connection with convex programming --- p.11Chapter 2.5 --- Chapter summary --- p.15Chapter 3 --- Implementation of the algorithm --- p.17Chapter 3.1 --- The new search direction --- p.17Chapter 3.2 --- Select the step-length --- p.23Chapter 3.3 --- The multi-constraint case --- p.25Chapter 3.4 --- Chapter summary --- p.32Chapter 4 --- Numerical results on randomly generated problem --- p.34Chapter 4.1 --- Single-constraint problems --- p.35Chapter 4.2 --- Multi-constraint problems --- p.36Chapter 4.3 --- Running time and the size of the problem --- p.39Chapter 4.4 --- Chapter summary --- p.42Chapter 5 --- Geometric optimization --- p.45Chapter 5.1 --- Geometric programming --- p.45Chapter 5.1.1 --- Monomials and posynomials --- p.45Chapter 5.1.2 --- Geometric programming --- p.46Chapter 5.1.3 --- Geometric program in convex form --- p.47Chapter 5.2 --- Conic transformation --- p.48Chapter 5.3 --- Computational results of geometric optimization problem --- p.50Chapter 5.4 --- Chapter summary --- p.55Chapter 6 --- Conclusion --- p.5

Scalable Coordinated Beamforming for Dense Wireless Cooperative Networks

To meet the ever growing demand for both high throughput and uniform coverage in future wireless networks, dense network deployment will be ubiquitous, for which co- operation among the access points is critical. Considering the computational complexity of designing coordinated beamformers for dense networks, low-complexity and suboptimal precoding strategies are often adopted. However, it is not clear how much performance loss will be caused. To enable optimal coordinated beamforming, in this paper, we propose a framework to design a scalable beamforming algorithm based on the alternative direction method of multipliers (ADMM) method. Specifically, we first propose to apply the matrix stuffing technique to transform the original optimization problem to an equivalent ADMM-compliant problem, which is much more efficient than the widely-used modeling framework CVX. We will then propose to use the ADMM algorithm, a.k.a. the operator splitting method, to solve the transformed ADMM-compliant problem efficiently. In particular, the subproblems of the ADMM algorithm at each iteration can be solved with closed-forms and in parallel. Simulation results show that the proposed techniques can result in significant computational efficiency compared to the state- of-the-art interior-point solvers. Furthermore, the simulation results demonstrate that the optimal coordinated beamforming can significantly improve the system performance compared to sub-optimal zero forcing beamforming