运筹学学报 ›› 2014, Vol. 18 ›› Issue (1): 69-92.

• 运筹学 • 上一篇    下一篇

线性与非线性规划算法与理论

戴彧虹1,*, 刘新为2   

  1. 1. 中国科学院数学与系统科学研究院,  北京 100190; 2. 河北工业大学理学院, 天津 300401
  • 出版日期:2014-03-15 发布日期:2014-03-15
  • 通讯作者: 戴彧虹 E-mail:dyh@lsec.cc.ac.cn
  • 基金资助:

    国家杰出青年科学基金 (No. 11125107), 国家自然科学基金资助项目 (Nos. \!11331012, 81173633, 11271107)

Advances in linear and nonlinear programming

DAI Yuhong1,*, LIU Xinwei2   

  1. 1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China; 2. Faculty of Science, Hebei University of Technology, Tianjin 300401, China
  • Online:2014-03-15 Published:2014-03-15

摘要:  线性规划与非线性规划是数学规划中经典而重要的研究方向.  主要介绍该研究方向的背景知识,并介绍线性规划、无约束优化和约束优化的最新算法与理论以及一些前沿与热点问题.  交替方向乘子法是一类求解带结构的约束优化问题的方法,近年来倍受重视. 全局优化是一个对于应用优化领域非常重要的研究方向. 因此也试图介绍这两个方面的一些最新研究进展和问题.

关键词: 线性规划, 非线性规划, 无约束优化, 约束优化, 交替方向乘子法, 全局优化

Abstract: Linear and nonlinear programming is a classical branch in mathematical programming. We introduce some backgrounds on linear and nonlinear programming, and some new methods and new research advances in linear programming, unconstrained and constrained optimization. The alternating direction method of multipliers is very efficient in solving some constrained optimization problems with special structure and has been attracted much attentions in recent years. Global optimization is specially important for applications of optimization. These two topics are also involved.

Key words: linear programming, nonlinear programming, unconstrained optimization, constrained optimization, alternating direction method of multipliers, global optimization

中图分类号: