绝对值方程和广义互补问题算法的研究

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17、x}ResearchAbouttheAbsoluteValueEquationandtheGeneralizedNonlinearComplementarityProblemABSTRACTThispapermainlystudiestheabsolutevalueequation(AVE)andthegen-eralizednonlinearcomplementa

18、rityproblem(GNCP)overthepolyhedralcone.Thestructureofthispaperisorganizedasfollows.Inchapter1,somedefinitionsandnotationsoftheabsolutevalueequationproblemandthegeneralizednonlinearcomplementarityproblemareintroduced.Then,wesummarizethemaincontentofthispaper

19、.Inchapter2,wediscussakindofabsolutevalueequationproblemAx−

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21、=b,A∈Rn×n,b∈Rn.WefirstreformulatethisproblemasasmoothingconvexLagrange-dualprogrammingandthensuggestanefficientmethodforsolvingit.Weshowthattheiterationsequencegeneratedbytheproposedalgorithmconver

22、gesgloballyinafiniteiterationsteps.Inchapter3,weconsiderthegeneralizednonlinearcomplementarityproblem(GNCP)overapolyhedralcone.Inthispaper,basedonaclassofsmoothingfunctions,asmoothingBroyden-likealgorithmisproposedforsolvingit.Un-dersuitableconditions,theit

23、erationsequencegeneratedbytheproposedalgo-rithmconvergesgloballyandsuperlinearly.Furthermore,thealgorithmhaslocalquadraticconvergenceundermildassumptions.Somenumericalexperimentsshowtheefficiencyoftheproposedal