中国数学规划学科发展概述

数学规划又称数学优化, 是运筹学的一个重要分支. 它主要研究在一定约束条件下, 如何求一个实数或者整数变量的实函数的最大值或者最小值. 它是运筹学和管理科学中最常用的一种建模工具和求解问题的方法, 在工程、经济和金融等领域有非常广泛的应用. 首先简单介绍数学规划的发展历史、应用领域及其主要研究方向; 然后简述数学规划的发展现状和在中国的发展进程; 最后, 讨论数学规划若干研究前沿问题与研究展望.

An overview of mathematical programming research in China

Mathematical programming or mathematical optimization is an important branch of operations research that studies the problem of minimizing or maximizing a real function of real or integer variables,  subject to constraints on the variables.  It is one of widely used modeling tools and methodologies in operations research and management science and has numerous applications in engineering, economics and finance.  In this chapter,  we first give a brief introduction of mathematical programming problems, its history, applications and main research areas.  We then review the state-of-the-science of mathematical programming study with an overview of the development of mathematical programming in China.  Research perspectives of mathematical programming is also presented.