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

针对最优控制中的核心问题之一--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分析。并将该算法应用于具体的网络资源分配问题，如功率分配、带宽分配等，并给出了数值算例。数值算例表明了该算法的有效性。该算法可以进行改进，使之适用于具有不完备性和非对称性的大规模复杂系统网络。

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.