Seeking strategy design for distributed nonsmooth games and its application

This paper investigates the nonsmooth noncooperative games (NGs) over unbalanced digraphs, where each player has a nondifferentiable payoff function. Meanwhile, these players are subject to local non -smooth inequality constraints, local convex set constraints and coupled equality constraints. Due to the coexistence of nonsmooth payoff functions, unbalanced digraphs and constraints, existing generalized Nash equilibrium (GNE) seeking strategies are fail to address our problem. Based on subgradient de-scents, differential inclusions, projection and primal-dual methods, we develop a distributed seeking strategy. Besides, the convergence of the strategy is proved. Finally, the proposed method is applied to electricity market games (EMGs) of smart grids.& COPY; 2023 The Franklin Institute. Published by Elsevier Inc. All rights reserved.

Automated summary

This paper investigates nonsmooth noncooperative games over unbalanced digraphs with non-differentiable payoff functions and various constraints. Existing generalized Nash equilibrium seeking strategies fail to address this complex problem. Therefore, a distributed seeking strategy based on subgradient descents, differential inclusions, projection, and primal-dual methods is proposed and proven to be convergent. The proposed method is also applied to electricity market games of smart grids.