Mathematical Sciences: Algorithms for Mathematical Programming

这个项目将开发、分析和实现解决数学规划问题的算法。计划将重点放在单纯形算法、内点算法以及它们的组合方法上。单纯形算法的研究将朝着解决网络流问题的方向发展，包括最大流、最小流、广义网络流问题和多商品流问题。内点算法的研究将集中于求解结构化线性规划、探索大步长路径跟踪算法、求解非线性规划问题。这项研究将包括算法的理论分析及其实现和实证测试。社会上需要运筹学的广泛领域将从这个项目中受益。

This project will develop, analyze, and implement algorithms for solving mathematical programming problems. It is planned to focus on simplex algorithms, interior point algorithms, and methods that combine them. The research on simplex algorithms will be directed towards solving network flow problems including maximum flow, minimum flow, generalized network flow problems, and multicommodity flow problems. The research on interior point algorithms will concentrate on solving structured linear programs, exploring large step path-following algorithms, solving nonlinear programming problems. This research will involve theoretical analysis of the algorithms and their implementation and empirical testing. Extensive areas of society where operations research is required will benefit from this project.