Matrix optimization problems for MIMO systems with matrix monotone objective functions
Matrix optimization problems for MIMO systems with matrix monotone objective functions
复制标题
具有矩阵单调目标函数的 MIMO 系统的矩阵优化问题
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Yiqing Zhou
中科院分区：
文献类型：
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作者：
C. Xing;Shaodan Ma;Yiqing Zhou
本文将多输入多输出（MIMO）系统的各种矩阵变量优化问题统一到一个新的优化框架中，即矩阵单调优化问题。单调性是函数最重要和最基本的特性之一，利用单调性可以得到和分析函数的最优解。在本文中，我们发现，在几种情况下，利用在半正定矩阵领域的单调性，所考虑的优化问题可以显着简化，例如，变量的维数从矩阵变量降为维数更低的向量变量。我们相信，就像凸性，单调性，特别是半正定矩阵，将有一个关键的作用，在未来的无线设计。
In this paper, various optimization problems with matrix variates for multiple-input multiple-output (MIMO) systems are unified into a novel optimization framework namely matrix-monotonic optimization problems. Monotonicity is one of the most important and fundamental characteristics of a function, which can be exploited to derive and analyze the optimal solutions. In this paper, we discover that in several cases taking advantage of the monotonicity in the field of positive semidefinite matrices, the considered optimization problems can be significantly simplified e.g., the dimensionality of the variables are reduced from matrix variates to be vector ones with much lower dimensionality. We believe that just like convexity, monotonicity, especially for positive semi-definite matrices, will have a critical role in the future wireless designs.