線(xiàn)性規(guī)劃原問(wèn)題與對(duì)偶問(wèn)題的轉(zhuǎn)化及其應(yīng)用

《線(xiàn)性規(guī)劃原問(wèn)題與對(duì)偶問(wèn)題的轉(zhuǎn)化及其應(yīng)用》由會(huì)員上傳分享，免費(fèi)在線(xiàn)閱讀，更多相關(guān)內(nèi)容在教育資源-天天文庫(kù)。

1、線(xiàn)性規(guī)劃原問(wèn)題與對(duì)偶問(wèn)題的轉(zhuǎn)化及其應(yīng)用摘要線(xiàn)性規(guī)劃對(duì)偶問(wèn)題是運(yùn)籌學(xué)中應(yīng)用較廣泛的一個(gè)重要分支，它是輔助人們進(jìn)行科學(xué)管理的一種數(shù)學(xué)方法.線(xiàn)性規(guī)劃對(duì)偶問(wèn)題能從不同角度為管理者提供更多的科學(xué)理論依據(jù)，使管理者的決定更加合理準(zhǔn)確.本文主要探討了線(xiàn)性規(guī)劃原問(wèn)題與對(duì)偶問(wèn)題之間的關(guān)系、線(xiàn)性規(guī)劃原問(wèn)題與對(duì)偶問(wèn)題的轉(zhuǎn)化以及對(duì)偶理論的應(yīng)用.本文的研究主要是將復(fù)雜的線(xiàn)性規(guī)劃原問(wèn)題轉(zhuǎn)化成對(duì)偶問(wèn)題進(jìn)行解決，簡(jiǎn)化了線(xiàn)性規(guī)劃問(wèn)題，使人們能夠快速的找出線(xiàn)性規(guī)劃問(wèn)題的最優(yōu)解.關(guān)鍵詞：線(xiàn)性規(guī)劃；原問(wèn)題；對(duì)偶問(wèn)題；轉(zhuǎn)化LinearProgrammingistheOrig

2、inalProblemandtheTransformationoftheDualProblemandApplicationsAbstract:Linearprogramminginoperationalresearchisresearchearlier,rapiddevelopmentandwideapplication,themethodisanimportantbranchofmature,itisoneofthescientificmanagementofauxiliarypeoplemathematicalmethod.Ca

3、nfromdifferentanglestolinearprogrammingdualproblemforpolicymakerstoprovidemorescientifictheorybasis.Thisarticlemainlyprobesintothelinearprogrammingproblemandtherelationshipbetweenthedualproblem,linearprogrammingproblemandthetransformationofthedualproblem,theapplication

4、oflinearprogrammingdualproblem.Thisarticleisthecomplexoftheoriginalproblemintoitsdualproblemtobesolved,simplifiesthelinearprogrammingproblem,enablesustorapidlyfindtheoptimalsolutionoflinearprogrammingproblem.Keywords:linearprogramming;theoriginalproblem;thedualproblem;

5、conversion目錄1引言12文獻(xiàn)綜述12.1國(guó)內(nèi)外研究現(xiàn)狀12.2國(guó)內(nèi)外研究現(xiàn)狀評(píng)價(jià)22.3提出問(wèn)題23預(yù)備知識(shí)23.1對(duì)稱(chēng)形式的原問(wèn)題23.2非對(duì)稱(chēng)形式的原問(wèn)題33.3對(duì)偶問(wèn)題的定義33.4原問(wèn)題轉(zhuǎn)化為對(duì)偶問(wèn)題的理論依據(jù)44原問(wèn)題與對(duì)偶問(wèn)題的轉(zhuǎn)化54.1原問(wèn)題與對(duì)偶問(wèn)題的關(guān)系54.2對(duì)稱(chēng)型原問(wèn)題化為對(duì)偶問(wèn)題64.3對(duì)稱(chēng)型對(duì)偶問(wèn)題轉(zhuǎn)換為原問(wèn)題94.4非對(duì)稱(chēng)型原問(wèn)題轉(zhuǎn)化為對(duì)偶問(wèn)題104.5對(duì)偶問(wèn)題的應(yīng)用135結(jié)論155.1主要發(fā)現(xiàn)155.2啟示155.3局限性155.4努力方向15參考文獻(xiàn)161引言線(xiàn)性規(guī)劃問(wèn)題是運(yùn)籌學(xué)里的一個(gè)重

6、要的分支，它的應(yīng)用比較廣泛，因而是輔助人們進(jìn)行現(xiàn)代科學(xué)管理的一種數(shù)學(xué)方法.隨著線(xiàn)性規(guī)劃理論的逐步深入，人們發(fā)現(xiàn)線(xiàn)性規(guī)劃問(wèn)題具有對(duì)偶性，即每一個(gè)線(xiàn)性問(wèn)題都伴有另外一個(gè)線(xiàn)性問(wèn)題的產(chǎn)生，兩者相互配對(duì)，密切聯(lián)系，反之亦然.我們把線(xiàn)性規(guī)劃的這個(gè)特性稱(chēng)為對(duì)偶性.于是，我們將其中的一個(gè)問(wèn)題稱(chēng)為原問(wèn)題，另一個(gè)問(wèn)題則稱(chēng)為它的對(duì)偶問(wèn)題.對(duì)偶性不僅僅是數(shù)學(xué)上的理論問(wèn)題，而且也是線(xiàn)性規(guī)劃中實(shí)際問(wèn)題的內(nèi)在經(jīng)濟(jì)聯(lián)系的必然反映.我們通過(guò)對(duì)對(duì)偶問(wèn)題的深入研究，發(fā)現(xiàn)對(duì)偶問(wèn)題能從不同角度對(duì)生產(chǎn)計(jì)劃進(jìn)行分析，從而使管理者能夠間接地獲得更多比較有用的信息.2文獻(xiàn)綜述2.1

7、國(guó)內(nèi)外研究現(xiàn)狀在所查閱到的國(guó)內(nèi)外參考文獻(xiàn)[1-15]中，有不少文章是探討了原問(wèn)題轉(zhuǎn)化為對(duì)偶問(wèn)題的方法以及對(duì)偶性質(zhì)的證明，并在對(duì)偶理論的應(yīng)用方面有所研究.如郝英奇，胡運(yùn)權(quán)在[1]、[10]中主要介紹了線(xiàn)性規(guī)劃中原問(wèn)題與對(duì)偶問(wèn)題中的一些基本概念，探究了實(shí)際問(wèn)題中的數(shù)學(xué)模型以及解.孫君曼，馮巧玲，孫慧君，李淑君等在[2]中探討了對(duì)偶理論中互補(bǔ)松弛定理在各種情況下的使用方法,使學(xué)生更好地掌握互補(bǔ)松弛定理的含義和應(yīng)用方法.胡運(yùn)權(quán)，郭耀煌，殷志祥等在[3]、[5]中系統(tǒng)的介紹了線(xiàn)性規(guī)劃中原始問(wèn)題與對(duì)偶問(wèn)題的兩種形式.郭鵬，徐玖平等在[6]、[8

8、]中用不同例子來(lái)說(shuō)明了原問(wèn)題轉(zhuǎn)化為對(duì)偶問(wèn)題的必要性.崔永新等在[9]、[15]中探討了對(duì)偶問(wèn)題的相關(guān)定理以及對(duì)偶問(wèn)題的可行解和最優(yōu)解之間的若干性質(zhì).李師正，王德勝在[11]中探討了如何用計(jì)算機(jī)計(jì)算對(duì)偶問(wèn)題的最優(yōu)解.岳宏志，藺小林，孫文