17251.線性互補問題的一個新的算法

1、⑧分類號盟工CS——學(xué)校代碼!Q!圣魚學(xué)號2Q12Q塑Z墨委￡～菱一≥萋內(nèi)蒙葛民癲大學(xué)碩士學(xué)位論文線性互補問題的一個新的算法NewMethodsforsolvingLinearcomplementarityproblems申請人：蘭英學(xué)科專業(yè)：應(yīng)用數(shù)學(xué)研究方向：優(yōu)化理論、方法及應(yīng)用學(xué)位類別：學(xué)術(shù)學(xué)位指導(dǎo)教師I韓海山教授論文提交日期：二。一五年五月NewMethodsforSolvingLinearcomplementarityProbl

2、emsAbstractThelinearcomplementarityproblemsstartfromthefieldofprojectphysics，mechanics，operationalresearchandeconomyIthaswidelyapplicationsinthequestionsofeconomicbalance。noncooperationcontest，trafficdistributionAnditisa

3、lsounificationinthequestionsoflinearprogramming，doublematrixgame，quadraticprogrammingTherefore，theresearchonLCPhastheoreticalsignificanceandapplicationvalueFirstly，accordingtOtheequivalenceoflinearcomplementaryproblemand

4、theabsolutevalueequation，thispapergivestheiterationmethodoftheabsolutevalueequationandprovesthepointseriesgenerateofthealgorithmconvergestothesolutionofLCP；Secondly，nonlinearpenalkizedequationsbasedonlinearcomplementarit

5、yproblem，weproposedthegeneralizedNewtonalgorithmofnonlinearpenalitizedequationssolvinglinearcomplementarityproblems，provesthatthealgorithmundercertainconditionsofconvergenceAndweshowconvergenceofthealgorithmbynumericalex

6、amplesThisthesisisdividedintothreechapters：Thefirstchapterintroducesthedefinitionofcomplementaryproblemandequivalenttransformation，anddescribestheabsolutevalueequationandpenaltyfunctionmethodThesecondchapterusestheequiva

7、lenceoflinearcomplementaryproblemandabsolutevalueequationbymatrixeigenvaluesofLCPgreaterthanzero，givestheiterationmethodofabsolutevalueequation。AndprovesthatpointseriesgenerateofthemethodconvergestothesolutionofLCPThethi

8、rdchapterusesthesufficientconditionsproposedinliterature[31]，whichguaranteesolutionofpenalizedequationconvergestothesolutionoftheLCPweproposeageneralizedNewtonalgorithmofnonlinearpenalizedequationundertheconditionthatint

9、ervalmatrixlA，A2／lisregularTherebybythatmeans，wesolvetheLCPandprovetheiterativealgorithmKeywords：Linearcomplementarityproblems；AbsolutevalueequationiNonlinearpenalizedequation；GeneralizedNewtonmethod“ConvergenceDirectedb