In this paper, we consider quantized distributed optimization problems with limited communication capacity and time-varying communication topology. A distributed quantized subgradient algorithm is presented with quantized information exchange between agents. Based on a proposed encoder-decoder scheme and a zooming-in technique, the optimal solution can be obtained without any quantization errors. Moreover, we explore how to minimize the quantization level number for quantized distributed optimization problems. In fact, the optimization problem can be solved with five-level quantizers in the switching topology case, while it can be solved with three-level quantizers in the fixed topology case.

In this paper, we investigate distributed generalized Nash equilibrium (GNE) computation of monotone games with affine coupling constraints. Each player can only utilize its local objective function, local feasible set and a local block of the coupling constraint, and can only communicate with its neighbours. We assume the game has monotone pseudo-subdifferential without Lipschitz continuity restrictions. We design novel center-free distributed GNE seeking algorithms for equality and inequality affine coupling constraints, respectively. A proximal alternating direction method of multipliers (ADMM) is proposed for the equality case, while for the inequality case, a parallel splitting type algorithm is proposed. In both algorithms, the GNE seeking task is decomposed into a sequential NE computation of regularized subgames and distributed update of multipliers and auxiliary variables, based on local data and local communication. Our two double-layer GNE algorithms need not specify the innerloop NE seeking algorithm and moreover, only require that the strongly monotone subgames are inexactly solved. We prove their convergence by showing that the two algorithms can be seen as specific instances of preconditioned proximal point algorithms (PPPA) for finding zeros of monotone operators. Applications and numerical simulations are given for illustration.

This paper investigates asynchronous algorithms for distributedly seeking generalized Nash equilibria with delayed information in multiagent networks. In the game model, a shared affine constraint couples all players' local decisions. Each player is assumed to only access its private objective function, private feasible set, and a local block matrix of the affine constraint. We first give an algorithm for the case when each agent is able to fully access all other players' decisions. By using auxiliary variables related to communication links and the edge Laplacian matrix, each player can carry on its iteration asynchronously with only private data and possibly delayed information from its neighbors. Then, we consider the case when agents cannot know all other players' decisions, called a partial-decision information case. We introduce a local estimation of the overall agents' decisions and incorporate consensus dynamics on these local estimations. The two algorithms do not need any centralized clock coordination, fully exploit the local computation resource, and remove the idle time due to waiting for the ``slowest'' agent. Both algorithms are developed by preconditioned forward-backward operator splitting, and their convergence is shown by relating them to asynchronous fixed-point iterations, under proper assumptions and fixed and nondiminishing step-size choices. Numerical studies verify the algorithms' convergence and efficiency.