简介：Inarecentarticle,theauthorsprovidedaneffectivealgorithmforbothcomputingtheglobalinfimumof/anddecidingwhetherornottheinfimumof/isattained,where/isamultivariatepolynomialoverthefieldRofrealnumbers.Asacomplement,theauthorsinvestigatethesemialgebraicallyconnectedcomponentsofminimumpointsofapolynomialfunctioninthispaper.Foragivenmultivariatepolynomial/overR,itisshownthattheabove-mentionedalgorithmcanfindatleastonepointineachsemi-algebraicallyconnectedcomponentofminimumpointsof/whenever/hasitsglobalminimum.

简介：Forill-posedbilevelprogrammingproblem,theoptimisticsolutionisalwaysthebestdecisionfortheupperlevelbutitisnotalwaysthebestchoiceforbothlevelsiftheauthorsconsiderthemodel'ssatisfactorydegreeinapplication.Toacquireamoresatisfyingsolutionthantheoptimisticonetorealizethetwolevels'mostprofits,thispaperconsidersbothlevels'satisfactorydegreeandconstructsaminimizationproblemofthetwoobjectivefunctionsbyweightedsummation.Then,usingthedualitygapofthelowerlevelasthepenaltyfunction,theauthorstransferthesetwolevelsproblemtoasingleoneandproposeacorrespondingalgorithm.Finally,theauthorsgiveanexampletoshowamoresatisfyingsolutionthantheoptimisticsolutioncanbeachievedbythisalgorithm.