lecture02

# lecture02 - Yinyu Ye MS&E Stanford MS&E211 Lecture...

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Unformatted text preview: Yinyu Ye, MS&E, Stanford MS&E211 Lecture Note #02 1 LinearProgramming YinyuYe DepartmentofManagementScienceandEngineering StanfordUniversity Stanford,CA94305,U.S.A. http://www.stanford.edu/˜yyye Yinyu Ye, MS&E, Stanford MS&E211 Lecture Note #02 2 SparsestDataFittingI Wewanttofindasparsestsolutiontofitexactdatameasurements,thatis,to minimizethenumberofnon-zeroentriesin x suchthat A x = b : minimize | support ( x ) | subjectto A x = b ; wherethesetfunction support ( x )= { j : x j 6 =0 } . Sometimesthisobjectivecanbeaccomplishedby minimize k x k 1 = ∑ n j =1 | x j | subjectto A x = b . Thisisa linearprogram ? Yinyu Ye, MS&E, Stanford MS&E211 Lecture Note #02 3 SparsestDataFittingII Yes,sinceitcanbeequivalentlyrepresentedby minimize ∑ n j =1 ¯ x j subjectto A x = b ,- ¯ x ≤ x ≤ ¯ x ; or minimize ∑ n j =1 ( x j + x 00 j ) subjectto A ( x- x 00 )= b . Yinyu Ye, MS&E, Stanford MS&E211 Lecture Note #02 4 LPExample5:CombinatorialAuctionI Given m potential states thataremutuallyexclusiveandexactlyoneofthemwill berealizedatthematurity. An order isabetononeora combination ofstates,witha pricelimit (the maximumpricetheparticipantiswillingtopayforoneunitoftheorder)anda quantitylimit (themaximumnumberofunitsorsharestheparticipantiswillingto...
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## This note was uploaded on 05/06/2010 for the course MSE 211 at Stanford.

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lecture02 - Yinyu Ye MS&E Stanford MS&E211 Lecture...

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