CAREER: Mixed Integer Programming-Parallelism and Applications to Statistical Analysis

本研究的主要重点是开发具有并行分布式计算能力的通用“工业强度”混合整数编程（MIP）代码，特别是允许在个人计算机集群或各种类型的工作站平台上并行执行的代码。研究的第二个重点是探索混合整数规划在判别分析问题中的新应用。最近开发的一个判别分析问题的MIP模型为接近这一重要的统计领域开辟了一条新的途径。人们正在研究这类问题的多面体结构，并开发出解决实际问题的有效策略。与研究计划相结合的是，一项协调一致的努力正在引起工程专业学生对数学规划（特别是整数规划）及其计算方面的更多兴趣。计划开设关于线性代数、并行计算和混合整数规划的新课程/研讨会。此外，正在努力建立与工业界的互动，从而使学生接触到为现实世界的问题建立和分析模型以及推导和解决方案的重要问题。

A major focus of this research is to develop a general ``industrial strength'' mixed integer programming (MIP) code with parallel distributed computing capability --- in particular, a code that allows parallel execution on clusters of personal computers or various types of workstation platforms. A second focus of the research is to explore new applications of mixed integer programming to problems in discriminant analysis. A recently developed MIP model of a problem in discriminant analysis opens up a new avenue for approaching this important area of statistics. The polyhedral structure of this class of problems is being investigated, and efficient strategies to solve real instances are being developed. In conjunction with the research plan, a concerted effort is being expended to arouse more interest in mathematical programming (especially integer programming) and its computational aspects among engineering students. New courses/seminars on linear algebra, parallel computation and mixed integer programming are planned. In addition, an effort is being made to establish interaction with industry, thereby exposing students to important issues in building and analyzing models for real-world problems and in deriving and solutions.