Structural Analysis of Mathematical Programming based on CombinatorialMatrix Theory

数学规划是研究最优化问题的一个分支，其目标是在一定的约束条件下寻求最优解，它可以应用于运筹学等工程领域。组合矩阵理论是用组合方法来理解矩阵结构的一种方法，它对大型线性系统的结构分析有着重要的实用价值。在这项研究中，我们分析了数学规划问题的基础上的组合属性，如符号模式或稀疏性。此外，我们还发展了组合矩阵理论在数学规划方面的应用。

Mathematical programming is a branch of mathematics concerned with optimization problems, in which one aims to find the best solution subject to some constraints, and it can be applied to a variety of engineering fields such as operations research. Combinatorial matrix theory is an approach to understand matrix structure using combinatorial methodology, which is useful for structural analysis of large linear systems in practice. In this research, we have analyzed mathematical programming problems based on combinatorial properties such as sign patterns or sparsity. In addition, we have developed combinatorial matrix theory in terms of mathematical programming applications.