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1、EDITEDBOOKTITLEEDITEDBYKLUWERACADEMICPUBLISHERSBoston/London/DordrechtCONTENTS1PIECEWISESEQUENTIALQUADRATICPROGRAMMINGFORMATHEMATICALPROGRAMSWITHNONLINEARCOMPLEMENTARITYCONSTRAINTSZhi-QuanLuo,Jong-ShiPang,DanielRalph11Introduction22Applicationtooptimaldesignofmechanicalstructu
2、res33ThePiecewiseSmoothApproachtoNCP-MP54ThePSQPmethodforNCP-MP105ComputationalTestingofPSQP15REFERENCES20vCONTRIBUTORSZhi-QuanLuoDept.ofElectricalandComputerEngi-neeringMcMasterUniversityHamilton,OntarioCANADAL8S4K1Jong-ShiPangDept.ofMathematicalSciencesTheJohnsHopkinsUnivers
3、ity,Baltimore,Maryland21218-2689,U.S.A.DanielRalphDepartmentofMathematicsTheUniversityofMelbourneParkville,Victoria3052,AUSTRALIA1PIECEWISESEQUENTIALQUADRATICPROGRAMMINGFORMATHEMATICALPROGRAMSWITHNONLINEARCOMPLEMENTARITYCONSTRAINTSZhi-QuanLuo*,Jong-ShiPang**,DanielRalphDepartm
4、entofMathematics,TheUniversityofMelbourne,Parkville,Victoria3052,Australia*McMasterUniversity,Hamilton,Ontario,Canada**TheJohnsHopkinsUniversity,Baltimore,Maryland,USAABSTRACTWedescribesome rst-andsecond-orderoptimalityconditionsformathematicalpro-gramswithequilibriumconstrain
5、ts(MPEC).Mathematicalprogramswithparamet-ricnonlinearcomplementarityconstraintsarethefocus.Ofinterestistheresultthatunderalinearindependenceassumptionthatisstandardinnonlinearprogramming,theotherwisecombinatorialproblemofcheckingwhetherapointisstationaryforanMPECisreducedtoche
6、ckingstationarityofsinglenonlinearprogram.Wealsopresentapiecewisesequentialquadraticprogramming(PSQP)algorithmforsolvingMPEC.Localquadraticconvergenceisshownunderthelinearindependenceassump-tionandasecond-ordersucientcondition.Somecomputationalresultsaregiven.KEYWORDSMPEC,bil
7、evelprogram,nonlinearcomplementarityproblem,nonlinearprogram, rst-andsecond-orderoptimalityconditions,linearindependenceconstraintquali- cation,sequentialquadraticprogramming,quadraticconvergence.12Chapter11INTRODUCTIONMathematicalProgramswithEquilibriumConstraints(MPEC)appear
8、inmany eldsfromeconomicstoengineering.See[9]forapplicationsan
