组合优化Considerafunctionf:whichislowersemicontinuousoverX,andassumethatisfiniteandoneofthefollowingthereconditionsholds:(1)pact.(2)pact.(3):LetbethesetofminimaoffoverX,.,,pact),thissequencehasatleastonelimitpointdenotedbysuchthatoneofitssubsequencestillexpressedasconvergestobyBolzano-,itislowersemicontinuouslyat,,wehavethat,.,,.,,wehave,,(2)holds,.,Thereexistsatleastonelevelset,say,,,,wehave,,wecanshowthatisclosedsimilarlyabove(1).Assumethatcondition(3),itsnonemptylevelsetsarebounded,socondition(2),:isaconvexfunction,,thenthereexistsatmostoneglobalminimumoffoverX..Proof:,,,forall(0,1),.Thus,fhasstrictlylowervaluethanatanypointonthelinesegmentconnectingwith,,thelinesegmentbelongstoX,,andassumetoarriveatacontradiction,thattwodistinctglobalminimaoffoverX,and,,,bythestrictoffoverX,-2+2+
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