凸优化的投影推和梯度下降-上升算法及其在经济调度中的应用
Projected Push-Sum Gradient Descent-Ascent for Convex Optimizationwith Application to Economic Dispatch Problems
摘要：
我们提出了一种新的算法求解凸，约束和分布式优化问题定义在多智能体网络，其中每个代理有独家访问的一部分，全球目标函数。代理能够通过有向加权通信图交换信息，该通信图可以表示为列随机矩阵。该算法结合了调整后的推和共识协议的信息扩散和梯度下降上升的局部代价函数，提供收敛到最佳的总和。我们提供的结果重新制定的推和成单一的矩阵更新，并证明该算法的收敛到一个最佳的解决方案，在分布式优化的标准假设。将该算法应用于一个分布式经济调度问题，其中的约束条件可以表示为局部和全局子集。
英文摘要：
We propose a novel algorithm for solving convex, constrained and distributed optimization problems defined on multi-agent-networks, where each agent has exclusive access to a part of the global objective function. The agents are able to exchange information over a directed, weighted communication graph, which can be represented as a column-stochastic matrix. The algorithm combines an adjusted push-sum consensus protocol for information diffusion and a gradient descent-ascent on the local cost functions, providing convergence to the optimum of their sum. We provide results on a reformulation of the push-sum into single matrix-updates and prove convergence of the proposed algorithm to an optimal solution, given standard assumptions in distributed optimization. The algorithm is applied to a distributed economic dispatch problem, in which the constraints can be expressed in local and global subsets.
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