Decentralized Hierarchical Constrained Convex Optimization
Decentralized Hierarchical Constrained Convex Optimization
复制标题
分散分层约束凸优化
DOI：
10.1007/s11081-019-09440-7
复制
发表时间：
2020
影响因子：
2.1
通讯作者：
Hideaki Iiduka
中科院分区：
文献类型：
--
作者：
K. Yamanaka;T. Horiyama;Y. Okamoto;R. Uehara;T. Yamauchi;畑中亮介，竹田晃人;Hideaki Iiduka
本文针对三层约束凸优化问题提出了一种分散优化算法，该问题最小化受非扩张映射不动点集交集上的副单调变分不等式约束约束的强凸函数之和。解决该问题的现有算法是利用问题中所有信息的集中优化算法，这些算法是有效的，但只有在某些附加限制下才有效。本文的主要贡献是对所提出的算法进行收敛分析，以表明所提出的使用步长递减序列的增量梯度的算法在没有任何额外限制的情况下收敛于问题的解决方案。本文的另一个贡献是阐明了网络资源分配和最优控制问题形式的分层约束优化的实际应用。特别是，它表明所提出的算法可以应用于具有三层结构的去中心化网络资源分配。
This paper proposes a decentralized optimization algorithm for the triple-hierarchical constrained convex optimization problem of minimizing a sum of strongly convex functions subject to a paramonotone variational inequality constraint over an intersection of fixed point sets of nonexpansive mappings. The existing algorithms for solving this problem are centralized optimization algorithms using all the information in the problem, and these algorithms are effective, but only under certain additional restrictions. The main contribution of this paper is to present a convergence analysis of the proposed algorithm in order to show that the proposed algorithm using incremental gradients with diminishing step-size sequences converges to the solution to the problem without any additional restrictions. Another contribution of this paper is the elucidation of the practical applications of hierarchical constrained optimization in the form of network resource allocation and optimal control problems. In particular, it is shown that the proposed algorithm can be applied to decentralized network resource allocation with a triple-hierarchical structure.