Convergence Analysis of Saddle Point Problems in Time Varying Wireless Systems - Control Theoretical Approach

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Saddle point problems arise from many wireless applications, and primal-dual iterative algorithms are widely applied to find the saddle points. In the existing literature, the convergence results of such algorithms are established assuming the problem specific parameters remain unchanged during the iterations. However, this assumption is unrealistic in time varying wireless systems, as explicit message passing is usually involved in the iterations and the Channel State Information (CSI) may change in a time scale comparable to the algorithm update period. This paper investigates the convergence behavior and the tracking error of primal-dual iterative algorithms under time varying CSI.