数据驱动的大规模结构型优化的分裂算法理论与应用研究

在大数据时代，数据驱动的大规模结构型优化有着重要的应用，因而受到了广泛的关注。算子分裂算法是求解该类优化模型最有效的方法之一，它采用化大为小、分而治之的策略将问题化难为易。应用算子分裂算法求解特殊的数据驱动结构型优化已经取得不少成果，但因该类优化模型的重要性和复杂性，我们仍需对更一般的数据驱动模型的分裂算法进行深入研究。本项目的研究工作包括：1）从变量块更新和算法加速等角度设计合理的分裂算法结构框架；2）从线性化和非精确计算等角度设计分裂算法子问题的快速求解方法；3）融合结构框架设计与子问题快速求解提出高效的算子分裂算法；4）针对非凸的数据驱动结构型优化设计有效的算子分裂算法；5）应用算法和理论结果解决数据驱动的设施选址问题。本项目包含算法设计、理论分析和应用研究，因此项目的实施不仅为求解大规模结构型优化提供理论与方法，同时也为解决大数据时代的实际问题提供支撑，具有重要的理论和应用价值。

In the era of big data, large-scale data-driven structured optimization has important applications, and thus it has attracted more and more attention. The operator splitting method is one of the most effective methods for this kind of optimization problem. Its key idea is to divide a large-scale problem into several small-scale subproblems and solve these subproblems independently, which will make the large-scale problem quite easier to solve than before. The operator splitting method has made a lot of achievements for particular data-driven structured optimization. Due to the importance and complexity of data-driven problems, however, further research on operator splitting method for general large-scale data-driven structured optimization is urgent. The research contents of this proposal include: 1) designing reasonable structure frameworks for operator splitting method from the perspective of block updating, algorithm acceleration and etc.; 2) designing fast methods for the subproblems of operator splitting method from the perspective of linearization, inexact calculation and etc.; 3) proposing efficient operator splitting methods with the combination of the aforementioned structure framework designing and subproblem solving; 4) proposing efficient operator splitting methods for nonconvex data-driven structured optimization; 5) applying the theoretical and algorithmic results to solve data-driven facility location problems. This proposal includes algorithm design, theoretical analysis and applied research, and thus its implementation not only provides numerical methods and theories for large-scale structured optimization, but also provides supports for practical problems in the era of big data. Therefore, this proposal is of significant importance both in theory and practice.