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1、Chapter4DistributedOptimizationandGames:ATutorialOverviewBoYangandMikaelJohanssonAbstract.Thischapterprovidesatutorialoverviewofdistributedoptimizationandgametheoryfordecision-makinginnetworkedsystems.WediscusspropertiesofÞrst-ordermethodsforsmoothandnon-smoothconvexoptimiz
2、ation,andreviewmathematicaldecompositiontechniques.Amodelofnetworkeddecision-makingisintroducedinwhichacommunicationstructureisenforcedthatdetermineswhichnodesareallowedtocoordinatewitheachother,andseveralrecenttechniquesforsolvingsuchproblemsarereviewed.Wethencontinuetostu
3、dytheimpactofnon-cooperativegames,inwhichnocommunicationandcoordinationareenforced.Spe-cialattentionisgiventoexistenceanduniquenessofNashequilibria,aswellastheefÞciencylossinnotcoordinatingnodes.Finally,wediscussmethodsforstudyingthedynamicsofdistributedoptimizationalgorith
4、msincontinuoustime.4.1IntroductionWeareinterestedinoptimizationalgorithmsthatcanbedistributedacrossmanydecision-makers.Theclassicalapproachtodistributedoptimizationhasbeendecomposition:basedonthespeciÞcstructureoftheobjectivefunctionandcon-straints,theproblemisdecomposedint
5、oanumberofsubproblems.Thesesub-problemscanbesolvedindependently,buttypicallyrequireacoordinatortoensurethatthelocaldecisionsconvergetotheglobaloptimum;seeFigure4.1.Notehowtheproblemstructureimposesacertaincomputationandcommunicationstructureamongtheindividualdecision-makers
6、.Inmanyemergingapplicationsofdistributedoptimization,however,thesitua-tionisthereverse:thecommunicationandcomputationstructureisgivenandtheBoYangDepartmentofAutomation,ShanghaiJiaoTongUniversity,Chinae-mail:bo.yang@sjtu.edu.cn,bo.yang@ieee.orgMikaelJohanssonSchoolofElectric
7、alEngineeringandACCESSLinnaeusCentere-mail:mikaelj@ee.kth.seA.Bemporad,M.Heemels,andM.Johansson:NetworkedControlSystems,LNCIS406,pp.109Ð148.springerlink.comcSpringer-VerlagBerlinHeidelberg2010110B.YangandM.JohanssonFig.4.1Schematicillustrationofcentralizedoptimization,deco
8、mposition,networkedopti-mizationandnon-cooperativeoptimizationimplementationofacen
