Springer.Borweinjm.Lewisas.2000.Convex.Analysis.N.Nonlinear.Optimization.Theory.N.Examples.Springer

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1、CONVEXANALYSISANDNONLINEAROPTIMIZATIONTheoryandExamplesJONATHANM.BORWEINCentreforExperimentalandConstructiveMathematicsDepartmentofMathematicsandStatisticsSimonFraserUniversity,Burnaby,B.C.,CanadaV5A1S6jborwein@cecm.sfu.cahttp://www.cecm.sfu.ca/∼jborweinandADR

2、IANS.LEWISDepartmentofCombinatoricsandOptimizationUniversityofWaterloo,Waterloo,Ont.,CanadaN2L3G1aslewis@orion.uwaterloo.cahttp://orion.uwaterloo.ca/∼aslewisToourfamilies2Contents0.1Preface...............................51Background71.1Euclideanspaces.........

3、................71.2Symmetricmatrices........................162Inequalityconstraints222.1Optimalityconditions.......................222.2Theoremsofthealternative...................302.3Max-functionsandfirstorderconditions............363Fenchelduality423.1Subgr

4、adientsandconvexfunctions...............423.2Thevaluefunction........................543.3TheFenchelconjugate......................614Convexanalysis784.1Continuityofconvexfunctions..................784.2Fenchelbiconjugation.......................904.3Lagrangia

5、nduality........................1035Specialcases1135.1Polyhedralconvexsetsandfunctions..............1135.2Functionsofeigenvalues.....................1205.3Dualityforlinearandsemidefiniteprogramming........1265.4Convexprocessduality......................1326Nons

6、moothoptimization1436.1Generalizedderivatives......................14336.2Nonsmoothregularityandstrictdifferentiability........1516.3Tangentcones...........................1586.4Thelimitingsubdifferential...................1677TheKarush-Kuhn-Tuckertheorem1767.1A

7、nintroductiontometricregularity..............1767.2TheKarush-Kuhn-Tuckertheorem...............1847.3Metricregularityandthelimitingsubdifferential........1917.4Secondorderconditions.....................1978Fixedpoints2048.1Brouwer’sfixedpointtheorem..............

8、....2048.2SelectionresultsandtheKakutani-Fanfixedpointtheorem..2168.3Variationalinequalities......................2279Postscript:infiniteversusfinitedimensions2389.1Introduction......