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1、EDITEDBOOKTITLEEDITEDBYKLUWERACADEMICPUBLISHERSBoston/London/DordrechtCONTENTS1PIECEWISESEQUENTIALQUADRATICPROGRAMMINGFORMATHEMATICALPROGRAMSWITHNONLINEARCOMPLEMENTARITYCONSTRAINTSZhi-QuanLuo,Jong-ShiPang,DanielRalph11Introduction22Applicationtooptimaldesignofmechanicals
2、tructures33ThePiecewiseSmoothApproachtoNCP-MP54ThePSQPmethodforNCP-MP105ComputationalTestingofPSQP15REFERENCES20vCONTRIBUTORSZhi-QuanLuoDept.ofElectricalandComputerEngi-neeringMcMasterUniversityHamilton,OntarioCANADAL8S4K1Jong-ShiPangDept.ofMathematicalSciencesTheJohnsHo
3、pkinsUniversity,Baltimore,Maryland21218-2689,U.S.A.DanielRalphDepartmentofMathematicsTheUniversityofMelbourneParkville,Victoria3052,AUSTRALIA1PIECEWISESEQUENTIALQUADRATICPROGRAMMINGFORMATHEMATICALPROGRAMSWITHNONLINEARCOMPLEMENTARITYCONSTRAINTSZhi-QuanLuo*,Jong-ShiPang**,
4、DanielRalphDepartmentofMathematics,TheUniversityofMelbourne,Parkville,Victoria3052,Australia*McMasterUniversity,Hamilton,Ontario,Canada**TheJohnsHopkinsUniversity,Baltimore,Maryland,USAABSTRACTWedescribesome rst-andsecond-orderoptimalityconditionsformathematicalpro-grams
5、withequilibriumconstraints(MPEC).Mathematicalprogramswithparamet-ricnonlinearcomplementarityconstraintsarethefocus.Ofinterestistheresultthatunderalinearindependenceassumptionthatisstandardinnonlinearprogramming,theotherwisecombinatorialproblemofcheckingwhetherapointissta
6、tionaryforanMPECisreducedtocheckingstationarityofsinglenonlinearprogram.Wealsopresentapiecewisesequentialquadraticprogramming(PSQP)algorithmforsolvingMPEC.Localquadraticconvergenceisshownunderthelinearindependenceassump-tionandasecond-ordersucientcondition.Somecomputati
7、onalresultsaregiven.KEYWORDSMPEC,bilevelprogram,nonlinearcomplementarityproblem,nonlinearprogram, rst-andsecond-orderoptimalityconditions,linearindependenceconstraintquali- cation,sequentialquadraticprogramming,quadraticconvergence.12Chapter11INTRODUCTIONMathematicalProg
8、ramswithEquilibriumConstraints(MPEC)appearinmany eldsfromeconomicstoengineering.See[9]forapplicationsan
