分式規(guī)劃和非凸二次規(guī)劃的分支定界算法研究.pdf

1、獨(dú)創(chuàng)性聲明本人聲明所呈交的論文是我個(gè)人在導(dǎo)師指導(dǎo)下進(jìn)行的研究工作及取得的研究成果盡我所知，除了文中特別加以標(biāo)注和致謝的地方外，論文中不包含其他人已經(jīng)發(fā)表或撰寫過的研究成果，也不包含為獲得寧夏大學(xué)或其它教育機(jī)構(gòu)的學(xué)位或證書而使用過的材料與我一同工作的同志對(duì)本研究所做的任何貢獻(xiàn)均已在論文中作了明確的說明并表示了謝意研究生簽名：任舒牟時(shí)間：糾多年月刁日關(guān)于論文使用授權(quán)的說明本人完全了解寧夏大學(xué)有關(guān)保留、使用學(xué)位論文的規(guī)定，即：學(xué)校有權(quán)保留送交

2、論文的復(fù)印件和磁盤，允許論文被查閱和借閱，可以采用影印、縮印或掃描等復(fù)制手段保存、匯編學(xué)位論文同意寧夏大學(xué)可以用不同方式在不同媒體上發(fā)表、傳播學(xué)位論文的全部或部分內(nèi)容(保密的學(xué)位論文在解密后應(yīng)遵守此協(xié)議)研究生簽名：任笥拜翩虢船水時(shí)間：2口／多年多月27日時(shí)間：)6哆年J月27日AbstractInourlife，manyimportantissuesarerelatedtotheselectionofthebestgoal0rsele

3、ctsomeparametersanddeterminecertainvaluesinordertoachievethegoal，theseproblemscanbeattributedtooptimizationproblemsThisthesismainlystudiesthealgorithmsofsolvingfractionalprogrammingandnon—convexquadraticprogrammingproble

4、msThethesisisdividedintothreepartsthebasiccontentsasfollows：Firstly，anewbranchandboundalgorithmisstudiedforsumoflinearfractionalprogrammingproblemInthisalgorithm，equivalenttransformationisusedontheoriginalproblemthenutil

5、izeanewlinearrelaxationlowerboundingmethod，makethenonconvexprogrammingproblemCanbeconvertedtoasequenceoflinearprogrammingproblems，ieobtainthelowerboundoftheoptimalvalueoftheoriginalproblemSecondly，abranchandboundreducedm

6、ethodisstudiedforgloballysolvingaclassofnon—convexquadraticprogrammingproblemwithlinearcons臼aintsTheequivalentproblemcanbeobtainedfromthecharacteristicsofaquadraticfunction，alinearrelaxationprogrammingoftheequivalentprob

7、lemcanbeconstructedbyusingtheconcaveenvelopesandconvexenvelopestechnique，ieobtainthelowerboundoftheoptimalvalueoftheoriginalproblem，theopt沛alsolutionsandtheoptimalvaluecanbeobtainedbysolvingasequenceoflinearrelaxationpro

8、grammingproblems，atthesametimeinordertoimprovetheapproximationofthealgorithmandacceleratetheconvergencerateofthealgorithm，thehyperrectangularreductiontechniqueisusedFinally，abranchandboundalgorithmisstudiedforgloballysol

9、vingaclassofnon—convexquadraticprogrammingproblemwithquadraticconstraintsAccordingtothecharacteristicsofaquadraticfunction，theinitialproblemisequivalentlytransformed，thenthelinearizationSoftheobjectivefunctionandconstrai

10、ntfunctionsisgivenbyusinganewlinearrelaxationtechniqueieobtainthelowerboundoftheoptimalvalueoftheoriginalproblem，thedegreeofapproximationandtheconvergencerateareimprovedthroughatwodeepersubdivisionandhyperrectangularredu

11、ctiontechniqueNumericalexperimentsarereportedtOshowthattheproposedalgorithmisfeasibleandeffectiveKeywords：globaloptimization；sumoflinearfractionalprogramming；non—convexquadraticprogramming；branchandboundmethod；linearrela