Efficient methods for large-scale structural optimization with application to machine learning

目前，结构优化问题经常出现在工程和科学领域，特别是在数据分析、机器学习和统计学领域。在大数据时代，这些问题往往是高维度的，并且在其目标和/或约束下包含大量的函数。这给传统的优化方法带来了前所未有的挑战。这项提案的目标是提出有效的方法并开发解决这些问题的软件，并探索它们在数据分析和机器学习中的应用。 提出的研究包括三个部分：1)开发在机器学习和统计学中有着广泛应用的函数的有限和最小化的有效方法；2)探索求解大规模结构优化问题的块坐标更新方法；3)研究求解大规模约束结构优化问题的有效方法。 该项目的成功将为解决大型结构优化问题提供有效的方法和软件。它们将帮助政府、金融机构、企业和行业使用更大的数据集，对未来做出更好的预测和决策，从而产生长期利益。这项拟议研究的成功还将导致新的优化理论和技术，以补充现有的持续优化知识。

Nowadays structural optimization problems frequently arise in engineering and sciences, especially in data analytics, machine learning and statistics. In big data era, these problems are often of high dimension and consist of large number of functions in their objective and/or constraints. This brings unprecedented challenges to traditional optimization methods. The objectives of this proposal are to propose efficient methods and develop software for solving them, and explore their applications in data analytics and machine learning. The proposed research consists of three parts: 1) developing efficient methods for minimization of a finite sum of functions that has numerous applications in machine learning and statistics; 2) exploring block coordinate updated methods for solving large-scale structural optimization problems; and 3) studying efficient methods for solving large-scale constrained structural optimization problems. The success of this project will provide efficient methods and software for solving large-scale structural optimization problems. They will help government, financial institutions, business and industry to use larger data sets to make a better prediction and decision for the future that will produce long-term benefits. The success of this proposed research will also result in new optimization theory and techniques that complement existing knowledge of continuous optimization.