Springer.Convex.Analysis.and.Non.Linear.Optimization.(Borwein.Lewis).[Springer.Verlag.2000].(273s)(1)

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

2、fCombinatoricsandOptimizationUniversityofWaterloo,Waterloo,Ont.,CanadaN2L3G1aslewis@orion.uwaterloo.cahttp://orion.uwaterloo.ca/∼aslewisToourfamilies2Contents0.1Preface...............................51Background71.1Euclideanspaces.........................71.2Symmetricmatrices.....

3、...................162Inequalityconstraints222.1Optimalityconditions.......................222.2Theoremsofthealternative...................302.3Max-functionsandfirstorderconditions............363Fenchelduality423.1Subgradientsandconvexfunctions...............423.2Thevaluefunction..

4、......................543.3TheFenchelconjugate......................614Convexanalysis784.1Continuityofconvexfunctions..................784.2Fenchelbiconjugation.......................904.3Lagrangianduality........................1035Specialcases1135.1Polyhedralconvexsetsandfunctio

5、ns..............1135.2Functionsofeigenvalues.....................1205.3Dualityforlinearandsemidefiniteprogramming........1265.4Convexprocessduality......................1326Nonsmoothoptimization1436.1Generalizedderivatives......................14336.2Nonsmoothregularityandstrictdiff

6、erentiability........1516.3Tangentcones...........................1586.4Thelimitingsubdifferential...................1677TheKarush-Kuhn-Tuckertheorem1767.1Anintroductiontometricregularity..............1767.2TheKarush-Kuhn-Tuckertheorem...............1847.3Metricregularityandthelimi

7、tingsubdifferential........1917.4Secondorderconditions.....................1978Fixedpoints2048.1Brouwer’sfixedpointtheorem..................2048.2SelectionresultsandtheKakutani-Fanfixedpointtheorem..2168.3Variationalinequalities......................2279Postscript:infiniteversusfinited

8、imensions2389.1Introduction......