Computational and Analytical Mathematics: In Honor of Jonathan Borwein's 60th Birthday PDF
Preview Computational and Analytical Mathematics: In Honor of Jonathan Borwein's 60th Birthday
Springer Proceedings in Mathematics & Statistics David H. Bailey · Heinz H. Bauschke Peter Borwein · Frank Garvan Michel Théra · Jon D. Vanderwerff Henry Wolkowicz Editors Computational and Analytical Mathematics In Honor of Jonathan Borwein's 60th Birthday Springer Proceedings in Mathematics & Statistics Volume 50 Forfurthervolumes: http://www.springer.com/series/10533 Springer Proceedings in Mathematics & Statistics Thisbookseriesfeaturesvolumescomposedofselectcontributionsfromworkshops and conferences in all areas of current research in mathematics and statistics, includingORandoptimization.Inadditiontoanoverallevaluationoftheinterest, scientific quality, and timeliness of each proposal at the hands of the publisher, individual contributions are all refereed to the high quality standards of leading journals in the field. Thus, this series provides the research community with well-edited, authoritative reports on developments in the most exciting areas of mathematicalandstatisticalresearchtoday. David H. Bailey • Heinz H. Bauschke Peter Borwein • Frank Garvan • Michel The´ra Jon D. Vanderwerff • Henry Wolkowicz Editors Computational and Analytical Mathematics In Honor of Jonathan Borwein’s 60th Birthday 123 Editors DavidH.Bailey HeinzH.Bauschke LawrenceBerkeleyNationalLaboratory DepartmentofMathematics Berkeley,CA,USA UniversityofBritishColumbia Kelowna,BC,Canada PeterBorwein DepartmentofMathematics FrankGarvan SimonFraserUniversity DepartmentofMathematics Burnaby,BC,Canada UniversityofFlorida Gainesville,FL,USA MichelThe´ra DepartmentofMathematics JonD.Vanderwerff Universite´deLimoges DepartmentofMathematics LimogesCedex,France andComputerScience LaSierraUniversity HenryWolkowicz Riverside,CA,USA FacultyofMathematics UniversityofWaterloo Waterloo,ON,Canada ISSN2194-1009 ISSN2194-1017(electronic) ISBN978-1-4614-7620-7 ISBN978-1-4614-7621-4(eBook) DOI10.1007/978-1-4614-7621-4 SpringerNewYorkHeidelbergDordrechtLondon LibraryofCongressControlNumber:2013945306 Mathematics Subject Classifications (2010): 05A15, 05E05, 11A63, 11K16, 11K45, 11M41, 11R06, 26B25,28Axx,28A80,28A25,33C20,37F10,41A65,46B10,46B26,46B50,46B20,46E30,46N10, 46T99, 47H04, 47A06, 47B65, 47H05, 47H09, 47H10, 47J05, 47J25, 47J20, 47N10, 49J52, 49J53, 49K27,49K40,49M27,49N15,52A27,52A41,52B55,54C15,58C06,58E17,58E30,65K05,90C22, 90C25,90C34,90C46,90C56,91A05,91B30,91G10,91G80 ©SpringerScience+BusinessMediaNewYork2013 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. 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Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Preface In the week of May 16–20, 2011, the workshop Computational and Analytical Mathematics (also known as JonFest) was held at the IRMACS Centre at Simon FraserUniversityinhonourofJonathanMichaelBorwein’s60thbirthday.Itbrought togethernearly100expertsfrom14countries. Jon Borwein is one of the most productive Canadian researchers ever. His researchinterestsarebroad,rangingfromanalysis,computationalmathematics,and optimizationto experimentalmathematicsand numbertheory.He has authoredor co-authoredmorethanadozenbooksandmorethan300papers. Those who have had the fortune of collaborating with him as students or colleagues will testify to his immense knowledge, technical mastery, and deep intuition. He has been altering the life trajectories of many of his collaborators significantly and sometimes dramatically. His passion and relentless pursuit for usefulandbeautifulmathematicsareextraordinary;thewayheinspiresandbrings outthebestinhisstudentsandcollaboratorsisSteveJobs-like! This book brings together 31 carefully refereed research and review papers in thebroadareasofJonBorwein’sinterests.Mostpapersinthisvolumegrewoutof talksdeliveredatJonFest;however,somecontributionsarefromexpertswhowere unabletoattend.Verysadly,oneofthecontributors,RichardCrandall,passedaway inDecember2012,beforethisbookwentintoproduction. We believe that the reader will find this book to be a delightful and valuable state-of-the-artaccountonsomefascinatingareasofComputationalandAnalytical Mathematics,rangingfromCantorfractalsandstronglynormalnumberstovarious algorithmsinoptimizationandfixedpointtheory. The editors thank the sponsors of JonFest—Interdisciplinary Research in the MathematicalandComputationalSciences(IRMACS)CentreatSimonFraserUni- versity(SFU),AustralianMathematicalSciencesInstitute(AMSI),Mathematicsof InformationTechnologyandComplexSystems(MITACS),PacificInstituteforthe Mathematical Sciences (PIMS), Fields Institute, and the Priority Research Centre forComputer-AssistedResearchMathematicsanditsApplications(CARMA)—for their financial and logistical support in hosting the workshop, and Pam Borghard v vi Preface andVeselinJungicfortheir“on-site”helpinthepreparationandrealizationofthe workshopattheIRMACSCentre. We are verygratefulto Dr. Hung Phan for his hard work and greathelp in the preparationofthisvolumewhichasaresultnotonlyisbeautifullytypesetbutalso exhibitsaconsistentstructure.WealsothankMs.ElizabethLoewfromSpringerfor herhelpguidingthisvolumethroughproduction. Finally, we thank the hardworking and dedicated referees who contributed crucially to the quality of this volume through their constructive and insightful reviews. Berkeley,(USA) DavidH.Bailey Kelowna,(Canada) HeinzH.Bauschke Burnaby,(Canada) PeterBorwein Gainesville,(USA) FrankGarvan Limoges,(France) MichelThe´ra Riverside,(USA) JonD.Vanderwerff Waterloo,(Canada) HenryWolkowicz Contents 1 NormalNumbersandPseudorandomGenerators...................... 1 DavidH.BaileyandJonathanM.Borwein 2 NewDemiclosednessPrinciplesfor(Firmly)Nonexpansive Operators.................................................................... 19 HeinzH.Bauschke 3 Champernowne’s Number, Strong Normality, andtheXChromosome.................................................... 29 AdrianBelshawandPeterBorwein 4 OptimalityConditionsforSemivectorialBilevelConvex OptimalControlProblems ................................................ 45 HenriBonnelandJacquelineMorgan 5 MonotoneOperatorsWithoutEnlargements............................ 79 JonathanM.Borwein,ReginaS.Burachik,andLiangjinYao 6 A Brøndsted–Rockafellar Theorem for Diagonal SubdifferentialOperators ................................................. 105 RaduIoanBo¸tandErno¨ RobertCsetnek 7 Aq-AnalogofEuler’sReductionFormulafortheDouble ZetaFunction ............................................................... 113 DavidM.BradleyandXiaZhou 8 FastComputationofBernoulli,TangentandSecantNumbers........ 127 RichardP.BrentandDavidHarvey 9 Monotone Operator Methods for Nash Equilibria inNon-potentialGames.................................................... 143 LuisM.Bricen˜o-AriasandPatrickL.Combettes 10 Compactness,Optimality,andRisk ...................................... 161 B.Cascales,J.Orihuela,andM.RuizGala´n vii viii Contents 11 LogarithmicandComplexConstantTermIdentities .................. 219 Tom Chappell, Alain Lascoux, S. Ole Warnaar, and WadimZudilin 12 Preprocessing and Regularization for Degenerate SemidefinitePrograms..................................................... 251 Yuen-LamCheung,SimonSchurr,andHenryWolkowicz 13 TheLargestRootsoftheMandelbrotPolynomials..................... 305 RobertM.CorlessandPiersW.Lawrence 14 OntheFractalDistributionofBrainSynapses.......................... 325 RichardCrandall† 15 VisiblePointsinConvexSetsandBestApproximation ................ 349 FrankDeutsch,HeinHundal,andLudmilZikatanov 16 OnDerivativeCriteriaforMetricRegularity........................... 365 AsenL.DontchevandHe´le`neFrankowska 17 FiveClassesofMonotoneLinearRelationsandOperators ........... 375 McleanR.Edwards 18 UpperSemicontinuityofDualityandPredualityMappings........... 401 J.R.Giles 19 ConvexityandVariationalAnalysis ...................................... 411 A.D.Ioffe 20 GenericExistenceofSolutionsandGeneric Well-PosednessofOptimizationProblems............................... 445 P.S.KenderovandJ.P.Revalski 21 LegendreFunctionsWhoseGradientsMapConvexSets toConvexSets............................................................... 455 AlexanderKnechtandJonVanderwerff 22 OntheConvergenceofIterationProcessesforSemigroups ofNonlinearMappingsinBanachSpaces ............................... 463 W.M.KozlowskiandBraileySims 23 TechniquesandOpenQuestionsinComputationalConvex Analysis...................................................................... 485 YvesLucet 24 ExistenceandApproximationofFixedPointsofRight BregmanNonexpansiveOperators....................................... 501 VictoriaMart´ın-Ma´rquez,SimeonReich,andShohamSabach 25 PrimalLowerNiceFunctionsandTheirMoreauEnvelopes.......... 521 MarcMazadeandLionelThibault Contents ix 26 Bundle Method for Non-ConvexMinimization with InexactSubgradientsandFunctionValues.............................. 555 DominikusNoll 27 ConvergenceofLinesearchandTrust-RegionMethods UsingtheKurdyka–ŁojasiewiczInequality ............................. 593 DominikusNollandAudeRondepierre 28 StrongDualityinConic LinearProgramming:Facial ReductionandExtendedDuals ........................................... 613 Ga´borPataki 29 TowardsaNewErainSubdifferentialAnalysis?....................... 635 Jean-PaulPenot 30 ModularEquationsandLatticeSums ................................... 667 MathewRogersandBoonrodYuttanan 31 AnEpigraph-BasedApproachtoSensitivityAnalysis inSet-ValuedOptimization................................................ 681 DouglasE.WardandStephenE.Wright
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