多维标度问题与方法是管理科学、统计学和最优化领域中一个共同关心的热点研究课题，其主要目的是通过对不同对象之间的相似性数据进行分析，从这些数据中发现其隐藏的内部规律并进行科学决策。它在分类学、管理学、经济学、测地学、地理学、遗传学、心理学、语言学、政治学、生物化学等多个学科领域有着广泛的应用。本项目旨在建立多维标度问题的矩阵优化模型与算法，研究内容包括：（1）从近几年蓬勃发展的矩阵优化角度，建立求解现代多维标度问题的各种优化模型，并讨论解的最优性条件、稳定性、灵敏性；（2）设计求解这些模型的各种优化算法，使之具有全局收敛性、稳定性、快速性；（3）对大规模多维标度实际问题（如道路网交通流数据分析）进行数值试验，从中选取优秀的算法并编制实用有效的数值软件。本项目的实施不仅能为求解多维标度问题提供新理论和新方法，而且也可为管理科学、统计学和最优化的交叉融合提供新元素，具有重要科学意义和实用价值。

Multidimensional Scaling (MDS) is a popular research topic of common interest in three areas of management science, statistics and optimization. It is a set of methods for discovering "hidden" structures in multidimensional data to make scientific decisions by analyzing the input data, which are typically a matrix of similarities measured on objects. Applications of MDS are found in a wide range of areas, including taxonomy, management, economics, geodesy, geography, genetics, psychology, linguistics, political science, biochemistry, etc. This project aims to establish matrix optimization models and algorithms for MDS, which in detail are as follows: (1) establish various optimization models for modern MDS and analyze the optimality conditions, stability and sensitivity; (2) design optimization algorithms which may have some properties of global convergence, stability and efficiency for the MDS models; (3) conduct numerical experiments for the large-scale MDS practical problems (such as traffic network data analysis), and choose the excellent algorithms to program efficient mathematical software. This project has scientific significance and practical values for not only providing new theory and methods for MDS, but also offering new elements for the cross areas of management science, statistics and optimization.