非凸优化的并行分布式方法--II：应用
Parallel and Distributed Methods for Nonconvex Optimization--Part II: Applications
摘要：
在本文的第一部分中，我们提出并分析了一种新的算法框架，最小化的非凸（光滑）的目标函数，受到非凸约束，基于内凸近似。这第二部分致力于应用的框架，在通信网络中的一些资源分配问题。特别是，我们考虑两个非平凡的案例研究应用，即：（概括）i）在MIMO干扰广播网络的速率配置文件最大化;和ii）在多小区环境中的最大-最小公平多播多组波束成形问题。我们开发了一类新的算法，具有以下独特的特征：i）它们是跨基站的\emph{distributed}（具有有限的信令），并导致其解可以以封闭形式计算的子问题;以及ii）不同于当前基于松弛的方案（例如，半定松弛），它们被证明总是收敛到上述非凸问题的d-平稳解。数值结果表明，所提出的（分布式）计划实现更大的最坏情况下的利率（分别为。信噪比干扰比），同时具有相当的计算复杂性。
英文摘要：
In Part I of this paper, we proposed and analyzed a novel algorithmic framework for the minimization of a nonconvex (smooth) objective function, subject to nonconvex constraints, based on inner convex approximations. This Part II is devoted to the application of the framework to some resource allocation problems in communication networks. In particular, we consider two non-trivial case-study applications, namely: (generalizations of) i) the rate profile maximization in MIMO interference broadcast networks; and the ii) the max-min fair multicast multigroup beamforming problem in a multi-cell environment. We develop a new class of algorithms enjoying the following distinctive features: i) they are \emph{distributed} across the base stations (with limited signaling) and lead to subproblems whose solutions are computable in closed form; and ii) differently from current relaxation-based schemes (e.g., semidefinite relaxation), they are proved to always converge to d-stationary solutions of the aforementioned class of nonconvex problems. Numerical results show that the proposed (distributed) schemes achieve larger worst-case rates (resp. signal-to-noise interference ratios) than state-of-the-art centralized ones while having comparable computational complexity.
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