A New Approach to Solving Nonlinear Programming

1　 IntroductionConsider a class of nonlinear programming problems as follows:max F( x1 ,x2 ,… ,xn)s.t.ai1 x1 ai2 x2 … ainxn=bi,i =1 ,2 ,… ,pai1 x1 ai2 x2 … ainxn bi,i =p 1 ,… ,mSuch nonlinear programming problems are wildly applied to the areas of engineering,economic management and even policy decision of the government,e.g.over-bounderyanalysis ofthe economy.Unfortunately,so far there is nota systemetic method to solvingsuch nonlinear programming problems.Only for some pro…     

A Way to Find All the Optimal Solutions in Linear Programming

1.INTRoDUCTIoNIngeneral,theoptimalsolutionsformedinactualbusinessmanagementsituationsprovidethebesteoforcemelltplansinthegivenpracticalproblems.Whenthereismoretha-noneoptimalsolutioninlinearprogramming,thereekistsunlimitednumberofoptimalsolutions.Tofindthemultipleoptimalsolutionsinlinearprogradringisaverysignificantwork,becausethedecisionmakercanbegivenmoreoptimalplanstochoosefrom.Sofar,therehavebeenmanypaPersdiscussingthesituationofunliIintedoptimalsolutions.However,therearendstthesandde…     

Order Structure Analysis（OSA） for the Optimal Solutions of Multiple Objective Mathematical Programming

ＯｒｄｅｒＳｔｒｕｃｔｕｒｅＡｎａｌｙｓｉｓ（ＯＳＡ）ｆｏｒｔｈｅＯｐｔｉｍａｌＳｏｌｕｔｉｏｎｓｏｆＭｕｌｔｉｐｌｅＯｂｊｅｃｔｉｖｅＭａｔｈｅｍａｔｉｃａｌＰｒｏｇｒａｍｍｉｎｇＦＥＮＧＪｕｎｗｅｎ（ＳｏｆｔＳｃｉｅｎｃｅＲｅｓｅａｒｃｈＩｎｓｔ...     

Determining the Optimal Solution Set for Linear Fractional Programming

1 .ＩＮＴＲＯＤＵＣＴＩＯＮＬｉｎｅａｒｆｒａｃｔｉｏｎａｌｐｒｏｇｒａｍｍｉｎｇｒｅｆｅｒｓｔｏｎｏｎｌｉｎｅａｒｐｒｏｇｒａｍｍｉｎｇｐｒｏｂｌｅｍｓｏｆｏｐｔｉｍｉｚｉｎｇｔｈｅｒａｔｉｏｏｆｔｗｏｌｉｎｅａｒｆｕｎｃｔｉｏｎｓｉｎｔｈｅｐｒｅｓｅｎｃｅｏｆｌｉｎｅａｒｃｏｎｓｔｒａｉｎｔｓ .Ｉｎｇｅｎｅｒａｌ,ｔｈｅｏｐｔｉｍａｌｓｏｌｕｔｉｏｎｏｆｔｈｅｍａｔｈｅｍａｔｉｃａｌｐｒｏｇｒａｍ ｍｉｎｇｆｏｒｍｅｄｉｎａｃｔｕａｌｂｕｓｉｎｅｓｓｍａｎａｇｅｍｅｎｔｓｉｔｕａｔｉｏｎｓｐｒ…     

The Uniqueness of Optimal Solution for Linear Programming Problem

This paper investigates an old problem in operations research, the uniqueness of the optimal solution to a linear programming problem. We discuss the problem on a general polyhedron, give some equivalent conditions for uniqueness testing. In addition, we discuss the implementation issues for linear programming based decision making procedures,which motivated this research.     

Optimal Approach to SAR Image Despeckling

1 .ＩＮＴＲＯＤＵＣＴＩＯＮＩｔｈａｓｂｅｅｎｆｏｕｎｄｔｈａｔａｌｍｏｓｔａｌｌｍｏｄｅｒｎｒａｄａｒｉｍａｇｅｓａｒｅｓｔａｔｉｓｔｉｃａｌｌｙｉｎｈｏｍｏｇｅｎｅｏｕｓ,ｗｈｉｃｈｒｅｓｕｌｔｓｆｒｏｍｔｈｅｈｉｇｈｓｐａｔｉａｌｒｅｓｏｌｕｔｉｏｎｉｎｍｏｄｅｒｎｒａｄａｒｓ.Ａｓａｈｉｇｈ ｒｅｓｏｌｕｔｉｏｎａｃｔｉｖｅｍｉｃｒｏｗａｖｅｓｅｎｓｏｒ,ＳＡＲ ,ｗｉｔｈｉｔｓａｂｉｌｉｔｙｔｏｉｍａｇｅｔｈｅＥａｒｔｈ’ｓｓｕｒｆａｃｅｉｎｎｅａｒｌｙａｌｌｗｅａｔｈｅｒｃｏｎｄｉｔｉｏｎ…     

A Multiple Model Approach to Modeling Based on LPF Algorithm

CONTROL THEORY AND APPLICATION1. INTRODUCTIONMost complex industrial processes may be characterized as non-linear and non-stationary. The colltrol methodsbased on linear models have then been challenged. Modeling and control of complex nonlinear systems becomesone of the difficult problems, which persecute control theory research and application. Several methods havebeen developed for known-structure system identification, including NARMAX, Hammerstein, Wiener or alsoHammers…     

Determination of Optimal Due-Date for Single-Machine Scheduling with Dynamic Programming Approach

1　ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｉｓｐａｐｅｒｃｏｎｓｉｄｅｒｓｔｈｅｐｒｏｂｌｅｍｏｆｄｕｅ ｄａｔｅａｓｓｉｇｎｍｅｎｔａｎｄｓｅｑｕｅｎｃｉｎｇｏｆａｓｅｔｏｆｎｉｎｄｅｐｅｎ ｄｅｎｔｊｏｂｓｏｎａｓｉｎｇｌｅｍａｃｈｉｎｅ .Ｄｕｅ ｄａｔｅｄｅｔｅｒｍｉｎａｔｉｏｎｈａｓｂｅｅｎａｐｏｐｕｌａｒｒｅｓｅａｒｃｈｔｏｐｉｃａｎｄｐｌｅｎｔｉｆｕｌｆｒｕｉｔｆｕｌｒｅｓｕｌｔｓｈａｖｅｂｅｅｎｏｂｔａｉｎｅｄｏｖｅｒｔｈｅｐａｓｔｙｅａｒｓ .Ｔｈｅｐｏｐｕｌａｒｉｔｙｏｆｓｃｈｅｄｕｌｉｎｇｒ…     

A New Approach to Optimal Filtering for SingularDiscrete-Time Stochastic Linear System

1IntroductionBecausetherealisticproblemwhichsingularsystemdescribesiswiderthanthenormalsystemsdo,theresearchofsingularsystemshasreceivedagreatdealofattention.Andmanyachievementshavebeenobtainedinthefieldsofstructuralcharacteranalysisanddesignmethodsofsingularsystems.Butforthestateestimationonlypreliminaryprobehasbeenmade.References[2]--[51proposedrespectivesolutionsbasedonleastsquaremethod.References[6]--[71transformsingularsystemsintonormalsystemsthroughmatrixresolutionandthenmakeuseofKalman…     

The Interactive Method: A New Approach to Solving a Kind of Mixed Integer Programming

Porduction planning often comes up in the form of programming problems with continuous variables, where investment project planing usually reduces to zero-one programming. Combination of the choices of investment projects with the existent production capacity, therefore, yields mixed integer programming. With this background, this paper provides a new approach to solving mixed integer programming problems by combining the man-machine interactive method for multiobjective programming with graphics generating techniques.     

一种求解多目标规划的新方法

以多目标规划理论和数据拟合法为基础,把两者有机结合起来,提出了一种求解多目标规划的新方法,并给出了详细的算法过程.该方法的特点是对所研究的多目标规划问题,无须决策者提供关于所研究问题的全部信息,却又兼顾了决策者的偏好,还简化了优化准则,实现了决策者与系统的信息交流及对规划过程的参与,具有一定的灵活性和一般性.     

基于多目标规划的扩展DEA有效性分析

为避免传统的DEA模型在评价决策单元的相对有效性存在的局限,建立了多目标规划的DEA模型(MP),讨论了MP的一些性质。在此基础上给出了关于决策单元的扩展DEA有效性的几个等价命题,并对决策单元扩展有效的灵敏度进行了讨论。     

多目标动态规划分层解法与Pareto最优解

本文指出了文[2]关于多目标动态规划分层解法结论的错误性, 证明了一个字典序最优解一定是Pareto最优解, 一个由分层解法得到的最优解一定为弱Pareto最优解, 并且可以通过修改分层解法得到的最优解集得到一个Pareto最优解集。     

油田措施配置多目标随机规划

措施规划对于延长油田稳产年限 ,合理地安排稳产措施从而提高采油速度及最终提高采收率是十分必要的 .有些学者建立了油田稳产措施规划的确定性规划 ,即模型中所有的参数均为确定值 ,而实际油田生产中有许多因素是不确定的 .也有文章建立了措施规划的随机规划模型 ,但建立的规划模型仅涉及一个目标函数 ,即所谓的单目标规划 .而在实际的油田措施配置中 ,需要对多项指标提出优化要求 .本文针对油田开发实际中存在的不确定现象 ,利用规划论中处理随机现象的机理 ,建立了油田措施的多目标随机规划模型 ,并采用具有擅长全局搜索、高度鲁棒性特点的遗传算法进行求解 .应用结果表明 ,该模型使措施配置更能反映生产实际.     

目的规划中的一个构造目标函数的方法

本文首先从理论上给出了一个目的规划问题中不同于“优先因子”法的构造单目标函数的方法。叫它做AHP赋政法。然后以人才规划为背景给出了一个实证例。     

工程系统多目标可靠度优化的几种方法

本文根据工程系统的各种目标要求,给出了两类多目标优化模型,并依次构造了三种可靠度优化的求解算法。算例表明,算法是很有效的。     

求解随机规划问题新方法——优劣解法

随机规划最优化,即使随机规划的目标函数最优化,达到最优值。那么怎样求随机规划目标函数的最优值呢?设随机规划问题min z=c′x,C为n维随机列向量,x为n维列向量,D为约束域。求其在满足约束条件下随机目标函数的最优值z~*=c′x~*。而如何判断随机变量是最小的呢?下面就此讨论,从而提出比较随机变量的方法。     

A Way to Find all the Optimal Solutions in Linear Programming

Ingeneral,theoptimalsolutionsformedinactualbusinessmanagementsituationsprovidethebestenforcementplansinthegivenpracticalproblems.Whenthereismorethanoneoptimalsolutioninlinearprogramming,thereexistsunlimitednumberofoptimalsolutions.Tofindthemultipleoptimalsolutionsinlinearprogrammingisaverysignificantwork,becausethedecisionmakercanbegivenmoreoptimalplanstochoosefrom.Sofar,therehavebeenmanypapersdiscussingthesituationofunlimitedoptimalsolutions.However,therearemistakesanddefectsinsomeofthem[1,2]…