幾類(lèi)廣義凸函數(shù)的性質(zhì)及其在最優(yōu)化問(wèn)題中的應(yīng)用.pdf

1、南昌航空大學(xué)碩士學(xué)位論文幾類(lèi)廣義凸函數(shù)的性質(zhì)及其在最優(yōu)化問(wèn)題中的應(yīng)用姓名：吳露申請(qǐng)學(xué)位級(jí)別：碩士專(zhuān)業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：邱根勝20080601IIABSTRACTIndertobreakthroughthelimitationsofconvexfunctionspromotetheirapplicationinpracticemanymathematicalresearchershavedefinedvariousgeneralized

2、convexfunctionssothattheycannotonlykeepexcellentacterofconvexfunctionbutalsoweakentheconvexityconditions.Thispapermainlyfocusesonseveralkindsofgeneralizedconvexfunctionsdiscussestheiractertheirapplicationstooptimization.

3、Firstlybasedon()h??convexitythispapergetstheoptimalityconditionsdualityfsolutionsoffractionalprogrammingwhichinvolvesinequalityequality.Secondlythisthesisdefinestheconceptof()h??nearlyconvexfunctionobtainssomepropertieso

4、fthematheemofalternativetodeducesomepropertiesofefficientsolutioninMultiobjectiveprogramming.Thirdlybasedupon()h??convexityconceptthispaperdefinesfourtypesofgeneralizedconvexfunctions:()h??quasiconvex()h??pointquasiconve

5、x()h??strictlyquasiconvex()h??strongquasiconvexobtainssomerelationshipofthemprovidescriteriaffunctionstobe()h??quasiconvex.Finallythispapergivesanoteondualityfmulationsofconvexprogrammingdiscussestherelationsamongfourdua

6、lityfmulationsofconvexprogramminggivesomesufficientconditionsftheirequivalence.Inconclusionthisthesisgeneralizesthecrespondingconclusionsoftheliteratureenrichesthecontentofgeneralizedconvexfunctionsstrengthenstheirapplic