面向大规模分布式一致性最优化问题的结构型一阶求解算法研究

项目名称： 面向大规模分布式一致性最优化问题的结构型一阶求解算法研究

项目编号： No.11501210

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 王祥丰

作者单位： 华东师范大学

项目金额： 18万元

中文摘要： 近年来，随着“大数据”处理需求的增加，大规模最优化问题受到了越来越多的关注。大规模分布式一致性最优化问题，因其结构特性以及在大规模机器学习等热门领域的优异表现，成为大规模优化的焦点问题之一。基于我们的前期工作，本项目旨在设计大规模结构型一阶算法高效求解大规模分布式一致性最优化问题，主要内容包括：（1）从分布式交替方向法入手，结合增量式、随机化、异步并行等计算技巧，设计问题结构驱动的高效分布式并行交替方向法，并分析算法框架理论性质;（2）将随机块坐标选择策略引入结构型并行算法框架，设计灵活的子问题求解方式，解决问题数据量与变量维度均大规模等问题;（3）将大规模结构型一阶算法框架应用到分布式机器学习与智能电网需求侧管理问题中，并结合Spark等大规模计算平台。该项目的实施不仅能为求解大规模分布式一致性最优化问题提供新方法，而且可为最优化、信息科学的交叉融合提供新元素，为学科发展做出切实的贡献。

中文关键词： 大规模优化问题；一阶算法；变分不等式；交替方向法；块坐标下降法

英文摘要： Recently, with the increasing demands for “Big Data” processing, large-scale optimization has received more and more attentions. The large-scale distributed consensus optimization problem becomes one of the hottest issues in large-scale optimization, because of its structure characteristics and excellent performance in large-scale machine learning and other popular research areas. Based on our preliminary work, the main purpose of this project is to design efficient large-scale structured first-order algorithms for large-scale distributed consensus optimization problems, which includes: (1) start from the distributed alternating direction method of multipliers (ADMM), combine with computing skills like the incremental, randomization, asynchronous parallel and etc., design problem-structure-driven efficient distributed parallel ADMM, and analyze the theory properties of the new algorithm framework; (2) introduce randomized block chosen strategy into the structured parallel algorithm framework, design flexible sub-problem computing patterns, and solve the problems with both large data size and large data dimension; (3) apply the large-scale structured first-order algorithm framework to the distributed machine learning and demand side management in smart grid, while mixing some large-scale computing platform like Spark and etc. The implementation of this project can not only provide new algorithms for solving large-scale distributed consensus optimization problems, but also provide new elements for the cross fusion of optimization and information science, which can make a tangible contribution to the development of the discipline.

英文关键词： Large-scale optimization problem;First-order method;Variational Inequality;Alternating direction method of multipliers;Block coordinate descent method