信号处理与通信中带线性和盒约束的凸可分问题
Convex separable problems with linear and box constraints in signal processing and communications
摘要：
在这项工作中，我们专注于可分离的凸优化问题的框约束和一组三角形线性约束。该解决方案是在封闭的形式，作为一个功能的一些拉格朗日乘子，可以计算通过迭代过程中的有限数量的步骤。图形解释铸造有价值的见解所提出的算法，并允许保留一些直观的注水政策。事实证明，它不仅足够通用，可以计算手头问题的不同实例的解决方案，而且操作方式非常简单。我们还展示了如何在信号处理和通信中的一些功率分配问题，可以解决所提出的算法。
英文摘要：
In this work, we focus on separable convex optimization problems with box constraints and a set of triangular linear constraints. The solution is given in closed-form as a function of some Lagrange multipliers that can be computed through an iterative procedure in a finite number of steps. Graphical interpretations are given casting valuable insights into the proposed algorithm and allowing to retain some of the intuition spelled out by the water-filling policy. It turns out that it is not only general enough to compute the solution to different instances of the problem at hand but also remarkably simple in the way it operates. We also show how some power allocation problems in signal processing and communications can be solved with the proposed algorithm.
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