Mathematical Sciences: Optimization Theory

本研究的一般主题领域是优化理论，特别是数学规划。 该研究的总体目标是促进对此类问题的根本属性的科学理解，开发解决各类数学规划问题的有效计算方法，并提出可以将所获得的知识用于造福科学和社会的方法。 该项目采用的方法将包括数学分析、开发和实验测试计算机软件，以数值解决现实问题。 数学规划涉及寻找具有许多变量以及对这些变量的许多约束的问题的最佳解决方案。 此类问题的实际应用几乎存在于科学技术的每个分支中。研究的目标是通过扩大可处理问题的规模、提高计算速度以及提高所得答案的实用性来扩展数学规划方法的范围并使其更加有效。

The general subject area of this research is optimization theory and mathematical programming in particular. The overall objectives of the research are to advance the scientific understanding of the underlying properties of such problems, to develop effective computational methods for solving various classes of mathematical programming problems, and to propose ways in which the knowledge acquired can be implemented for the benefit of science and society. The methods employed in this project will include mathematical analysis, development and experimental testing of computer software for numerical solution of real-world problems. Mathematical programming is concerned with finding the best solution to problems with many variables and many constraints on such variables. Practical applications of such problems are found in virtually every branch of science and technology. The goal of the research is to extend the scope of mathematical programming methods and to make them more effective by enlarging the size of problems that can be handled, increasing the speed with which the computing is done, and improving the usefulness of the answers obtained.