We present a novel generalized constrained convex optimization model for multiagent systems that contains both the local, coupled equality, and inequality constraints, and a global resource allocation constraint. This model unifies the traditional constrained optimization problem, the resource allocation problem, and the economic dispatch problem. Unlike the majority of literature where each local objective function is required to be convex, we only require a milder condition that the global objective function is convex. The gradient of the global Lagrangian is estimated locally by each agent using the dynamic average consensus protocol. Synchronously, modified primal-dual dynamics produce the optimal solution via the estimated gradient. The generalized Lagrange multiplier method is introduced to avoid the usual positive projections in the presence of inequality constraints. This leads to smooth dynamics and a continuous Lyapunov derivative, which enables the exponential stability analysis. Simulation examples support the proposed distributed methods.

中文翻译：

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具有非凸局部目标函数和资源分配约束的无投影分布式优化

我们为多主体系统提出了一种新颖的广义约束凸优化模型，该模型同时包含局部，耦合等式和不等式约束，以及全局资源分配约束。该模型统一了传统的约束优化问题，资源分配问题和经济调度问题。与大多数文献都要求每个局部目标函数都是凸的不同，我们只需要一个较为温和的条件，即全局目标函数是凸的。每个代理商使用动态平均共识协议在本地估计全局拉格朗日梯度。同步地，修改后的原始对偶动力学通过估计的梯度产生最佳解决方案。引入广义拉格朗日乘数法来避免存在不等式约束时通常的正投影。这导致平滑的动力学和连续的Lyapunov导数，从而可以进行指数稳定性分析。仿真示例支持所提出的分布式方法。