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优化问题与线性逼近解法
引用本文:赖炎连.优化问题与线性逼近解法[J].咸宁学院学报,2001,21(3):1-9.
作者姓名:赖炎连
作者单位:中国科学院数学与系统科学研究院应用数学研究所,
摘    要:本概要地介绍了运筹学的重要分支——最优化的研究背景及作为基础方法的线性逼近解法,中首先介绍线性规划及名的G.B.Dantzig单纯形方法,随后介绍了基于线性规划解法的线性逼近即Frank—wolfe方法以及基于投影概念的求解带非线性等式与不等式约束条件的优化问题的广义投影算法.只要掌握了线性规划的建模及解法,就能应用于许多实际问题.对于大型问题,目前国内已有相应的解题软件.

关 键 词:运筹学  优化问题  线性逼近法  广义投影算法
文章编号:1006-5342(2001)03-0001-09
修稿时间:2001年4月6日

Optimization Problem and Linearly Approximate Algorithm
LAI Yan-lian.Optimization Problem and Linearly Approximate Algorithm[J].Journal of Xianning College,2001,21(3):1-9.
Authors:LAI Yan-lian
Abstract:Optimization is an important branch of Operational Research.In this paper,an outline of background about Optimization is given and some algorithms with linear approximation are introduced.First,famous simplex method of linear programming by G.B.Dantzig is introduced.And then Frank-Wolfe method based on linear programming,generalized gradient projection algorithm based on projection technique for nonlinear optimization with nonlinear constraints are introduced.Linear programming has wide application fields.Now ,there has been developed software for solving large-scale linear programming in China.
Keywords:Operational Research  Optimization problem  Linearly approximate method  Generalized projection algorithm
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