Fixed point optimization algorithm and its application to linear-quadratic control problems

针对最优控制的核心问题之一线性二次控制问题，我们设计了一种迭代算法，称为不动点优化算法，并对该算法进行了收敛性分析。将该算法应用于具体的网络资源分配问题，如功率和带宽的分配，并给出了这些问题的数值算例。算例表明了该算法的有效性。提出的算法可以被修改，以适用于具有不完备性和不对称性的大型复杂系统网络。

We devised an iterative algorithm, called a fixed point optimization algorithm, for solving a linear-quadratic control problem, which is one of the central issues in optimal control and conducted a convergence analysis on the algorithm. We also applied the algorithm to concrete network resource allocation problems such as power and bandwidth allocation and provided numerical examples for these problems. The numerical examples showed the effectiveness of the algorithm. The proposed algorithm may be modified to work for large-scale and complex system networks with incompleteness and asymmetry.