[博弈论书籍].convex.optimization,game.theory,and.variational.inequality.theory,2010

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1、[GesualdoScutari,DanielP.Palomar,FranciscoFacchinei,andJong-ShiPang][Basictheoreticalfoundationsandmaintechniquesinmultiusercommunicationsystems]heuseofoptimizationmethodsisubiquitousincom-municationsandsignalprocessing.Inparticular,con-vexoptimizationtechniqueshavebeenwidelyusedinthedesign

2、andanalysisofsingleuserandmul-Ttiusercommunicationsystemsandsignalprocess-ingalgorithms(e.g.,[1]and[2]).Gametheoryisafieldofappliedmathematicsthatdescribesandanalyzesscenarioswithinteractivedecisions(e.g.,[3]and[4]).Roughlyspeak-ing,agamecanberepresentedasasetofcoupledoptimi-zationproblems.

3、Inrecentyears,therehasbeenagrowinginterestinadoptingcooperativeandnoncooperativegametheoreticapproachestomodelmanycommunicationsandnetworkingproblems,suchaspowercontrolandresourcesharinginwireless/wiredandpeer-to-peernetworks(e.g.,[5]–[12]),cognitiveradiosystems(e.g.,[13]–[17]),anddistribut

4、edrouting,flow,andcongestioncontrolincom-municationnetworks(e.g.,[18]and[19]andreferencestherein).Tworecentspecialissuesonthesubjectare[20]and[21].Amoregeneralframeworksuitableforinvestigat-ingandsolvingvariousoptimizationproblemsandequilibri-ummodels,evenwhenclassicalgametheorymayfail,iskn

5、owntobethevariationinequality(VI)problemthatconsti-tutesaverygeneralclassofproblemsinnonlinearanalysis[22].MOTIVATIONThegoalofthisarticleistwofold.Thefirsthalfaimsatpresentinginaunifiedfashionthetheoreticalfoundationsandmaintechniquesinconvex©BRANDXPICTURESoptimization,gametheory,andVItheor

6、y,suitableforthecommunicationandDigitalObjectIdentifier10.1109/MSP.2010.9360211053-5888/10/$26.00©2010IEEEIEEESIGNALPROCESSINGMAGAZINE[35]MAY2010signalprocessingcommunities.Specialemphasisisplacedon■convexonKif,4x,y[Kanda[10,12,thegeneralityoftheVIframework,showinghowseveralinter-estingprob

7、lemsinnonlinearanalysis,optimization,andequi-f1ax1112a2y2#af1x21112a2f1y2(2)libriumprogrammingcanbeformulatedasaVIproblem,suchasnonlinear(convex)optimizationproblems[22]and(general-■strictlyconvexonKiftheinequalityin(2)isstrictized)Nashequilibriumproblem