Foundations of a strong monotonicity theorem

Current monotonicity analysis of optimization problems has loose ends and ... This leads to a simple and clear `Strong' Monotonicity Theorem giving ... SignIn ViewCart Help EmailorUsername Forgotyourusername? Password Forgotyourpassword? Show Keepmesignedin Pleasewait... NoSPIEaccount?Createanaccount InstitutionalAccess:Signinwithyourinstitutionalcredentials TranslatorDisclaimer Youhaverequestedamachinetranslationofselectedcontentfromourdatabases.Thisfunctionalityisprovidedsolelyforyourconvenienceandisinnowayintendedtoreplacehumantranslation.NeitherSPIEnortheownersandpublishersofthecontentmake,andtheyexplicitlydisclaim,anyexpressorimpliedrepresentationsorwarrantiesofanykind,including,withoutlimitation,representationsandwarrantiesastothefunctionalityofthetranslationfeatureortheaccuracyorcompletenessofthetranslations. Translationsarenotretainedinoursystem.YouruseofthisfeatureandthetranslationsissubjecttoalluserestrictionscontainedintheTermsandConditionsofUseoftheSPIEwebsite. 22March1996 Foundationsofastrongmonotonicitytheorem DouglassJ.Wilde AuthorAffiliations+ DouglassJ.Wilde1 1StanfordUniv.(UnitedStates) ProceedingsVolume2644,FourthInternationalConferenceonComputer-AidedDesignandComputerGraphics;(1996)https://doi.org/10.1117/12.235508Event:FourthInternationalConferenceonComputer-AidedDesignandComputerGraphics,1995,Wuhan,China ARTICLE CITEDBY DOWNLOADPAPER SAVETOMYLIBRARY PERSONALSIGNIN Fullaccessmaybeavailablewithyoursubscription EmailorUsername Forgotyourusername? Password Forgotyourpassword? 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CreateNewFolder SAVE> FolderName FolderDescription SAVE Abstract Currentmonotonicityanalysisofoptimizationproblemshaslooseendsandloopholeswhichconfusetheunderstanding,teachinganduseofthetechniques.Theseembarrassmentsareremovedinthisarticlebyredefiningslightlythedomain,theobjectiveandconstraintfunctions,andeventhenotionofcriticalityitself.Thisleadstoasimpleandclear`Strong'MonotonicityTheoremgivingextensionsofthetwomonotonicityprinciplesarestraightforwardcorollaries.ThistheoremnotonlyincorporatesHansen,JaumardandLu'sextensionstonon-monotonicfunctions,butalsoclarifiesthespecialeliminationrulesapplicabletovariablesintheconstraintsbutnottheobjective.Thissetsthestageforanalyzingoptimizationproblemswithnon-monotonicfunctions. ©(1996)COPYRIGHTSocietyofPhoto-OpticalInstrumentationEngineers(SPIE).Downloadingoftheabstractispermittedforpersonaluseonly. Citation DownloadCitation DouglassJ.Wilde "Foundationsofastrongmonotonicitytheorem",Proc.SPIE2644,FourthInternationalConferenceonComputer-AidedDesignandComputerGraphics,(22March1996);https://doi.org/10.1117/12.235508 ACCESSTHEFULLARTICLE PERSONALSIGNIN Fullaccessmaybeavailablewithyoursubscription EmailorUsername Forgotyourusername? Password Forgotyourpassword? 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CLOSE DouglassJ.Wilde,"Foundationsofastrongmonotonicitytheorem,"Proc.SPIE2644,FourthInternationalConferenceonComputer-AidedDesignandComputerGraphics,(22March1996);https://doi.org/10.1117/12.235508 Include: CitationOnly Citation&Abstract Format: RIS(Zotero) EndNote BibTex Medlars ProCite RefWorks DOWNLOADCITATION CONFERENCEPROCEEDINGS Papers Presentations Journals AdvancedPhotonics AdvancedPhotonicsNexus JournalofAppliedRemoteSensing JournalofAstronomicalTelescopes,Instruments,andSystems JournalofBiomedicalOptics JournalofElectronicImaging JournalofMedicalImaging JournalofMicro/Nanopatterning,Materials,andMetrology JournalofNanophotonics JournalofOpticalMicrosystems JournalofPhotonicsforEnergy Neurophotonics OpticalEngineering PhotonicsInsights Ebooks Help| AdvancedSearch> Keywords/Phrases Keywords in AllFields Abstract AuthorName Affiliation DOI/ISSN/ISBN Figure&TableCaptions Keywords Title VolumeTitle Remove AND OR NOT in AllFields Abstract AuthorName Affiliation DOI/ISSN/ISBN Figure&TableCaptions Keywords Title VolumeTitle Remove AND OR NOT in AllFields Abstract AuthorName Affiliation DOI/ISSN/ISBN Figure&TableCaptions Keywords Title VolumeTitle Remove +Addanotherfield SearchIn: Proceedings Volume Journals+ Volume Issue Page AdvancedPhotonics JournalofAppliedRemoteSensing JournalofAstronomicalTelescopesInstrumentsandSystems JournalofBiomedicalOptics JournalofElectronicImaging JournalofMedicalImaging JournalofMicro/Nanopatterning,Materials,andMetrology JournalofNanophotonics JournalofPhotonicsforEnergy JournalofOpticalMicrosystems Neurophotonics OpticalEngineering SPIEReviews eBooks+ FieldGuideSeries PressMonograph Spotlight TutorialText OtherPress PublicationYears Range SingleYear ClearForm