Distributed Generalized Aggregative Equilibrium Seeking via Inexact Krasnosel’skii-Mann Iteration Over Time-Varying Communication Graphs

Abstract

This paper investigates the generalized aggregative equilibrium (GAE) under globally-shared affine coupling constraints within the context of aggregative games involving a collective of agents. Specifically, the study is centered on a non-smooth composite game scenario, wherein each agent possesses a local Lipschitz- differentiable function coupled with a lower semi-continuous function. Utilizing the operator splitting technique, the dynamic tracking method and the successive approximation theorem, we progressively formulate three GAE seeking algorithms from requiring full decision information to partial decision information. These algorithms leverage the local, time-varying communication framework and the deployment of splitting operators characterized by maximal monotone, alleviate the stringent requirement for strongly monotone. By employing the inexact Krasnosel’skii-Mann (KM) iteration and the aggregation invariance, we derive strict bounds on the non-vanishing iterative steps, establishing convergence toward the variational GAE (v-GAE). Finally, the effectiveness and superiority of the proposed algorithms are demonstrated through their application to the time-varying networked Nash-Cournot game model.