In this article, we consider a network of processors aiming at cooperatively solving mixed-integer convex programs subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set. We propose a randomized, distributed algorithm working under asynchronous, unreliable, and directed communication. The algorithm is based on a local computation and communication paradigm. At each communication round, nodes perform two updates: 1) A verification in which they check—in a randomized fashion—the robust feasibility of a candidate optimal point, and 2) an optimization step in which they exchange their candidate basis (the minimal set of constraints defining a solution) with neighbors and locally solve an optimization problem. As a main result, we show that processors can stop the algorithm after a finite number of communication rounds (either because verification has been successful for a sufficient number of rounds or because a given threshold has been reached) so that candidate optimal solutions are consensual. The common solution has proven to be—with high confidence—feasible and, hence, optimal for the entire set of uncertainty except a subset having an arbitrarily small probability measure. We show the effectiveness of the proposed distributed algorithm using two examples: a random, uncertain mixed-integer linear program and a distributed localization in wireless sensor networks. The distributed algorithm is implemented on a multicore platform in which the nodes communicate asynchronously.

中文翻译：

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分布式鲁棒混合整数规划的随机约束共识

在本文中，我们考虑了一个处理器网络，旨在合作解决不确定性下的混合整数凸程序。每个节点仅知道一个公共成本函数及其局部不确定约束集。我们提出了一种在异步，不可靠和定向通信下工作的随机，分布式算法。该算法基于本地计算和通信范例。在每个通信回合中，节点执行两次更新：1）验证，其中他们以随机方式检查候选最佳点的鲁棒性，以及2）优化步骤，在该步骤中，他们交换候选基础（最小集合）与邻居定义约束的解决方案），并在本地解决优化问题。主要结果是 我们表明，处理器可以在有限数量的通信回合后停止算法（因为验证已成功进行了足够的回合数或已达到给定的阈值），因此候选最佳解决方案是可以达成共识的。事实证明，通用解决方案是可行的，因此具有很高的置信度，因此，除了子集具有任意小的概率测度外，它对于整个不确定性集都是最佳的。我们使用两个示例展示了所提出的分布式算法的有效性：随机，不确定的混合整数线性程序和无线传感器网络中的分布式定位。分布式算法是在节点异步通信的多核平台上实现的。