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Zeroth-Order Method for Distributed Optimization With Approximate Projections

机译:近似投影分布优化的零阶方法

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This paper studies the problem of minimizing a sum of (possible nonsmooth) convex functions that are corresponding to multiple interacting nodes, subject to a convex state constraint set. Time-varying directed network is considered here. Two types of computational constraints are investigated in this paper: one where the information of gradients is not available and the other where the projection steps can only be calculated approximately. We devise a distributed zeroth-order method, the implementation of which needs only functional evaluations and approximate projection. In particular, we show that the proposed method generates expected function value sequences that converge to the optimal value, provided that the projection errors decrease at appropriate rates.
机译:本文研究了在凸状态约束集的约束下最小化对应于多个交互节点的(可能是非光滑的)凸函数之和的问题。这里考虑时变定向网络。本文研究了两种类型的计算约束:一种类型的梯度信息不可用,另一种类型的投影步长只能近似计算。我们设计了一种分布式零阶方法,其实现仅需要功能评估和近似投影。特别是,我们证明了所提出的方法会产生收敛到最佳值的期望函数值序列,前提是投影误差以适当的比率减小。

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