convex analysis and non linear optimization theory and examples - borwein,lewis

《convex analysis and non linear optimization theory and examples - borwein,lewis》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

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

2、ombinatoricsandOptimizationUniversityofWaterloo,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........................1035Specialcases1135.1Polyhedralconvexsetsandfunctions......

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

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

7、ential........1917.4Secondorderconditions.....................1978Fixedpoints2048.1Brouwer’sfixedpointtheorem..................2048.2SelectionresultsandtheKakutani-Fanfixedpointtheorem..2168.3Variationalinequalities......................2279Postscript:infiniteversusfinitedimensions2389.

8、1Introduction......