optimization by variational methods (morton m. denn)

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1、OPTIMIZATIONBYVARIATIONALMETHODSMORMONM.DENNOPTIMIZATIONBYVARIATIONALMETHODSMORTONM.DENNAssociateProfessorofChemicalEngineeringUniversityofDelawarePrefaceThedevelopmentofasystematictheoryofoptimizationsincethemid-1950shasnotbeenfollowedbywidespreadapplicationtothedesignan

2、dcontrolproblemsoftheprocessindustries.Thissurprisinganddisap-pointingfactislargelyaconsequenceoftheabsenceofeffectivecommuni-cationbetweentheoristsandprocessengineers,forthelattertypicallydonothave,sufficientmathematicaltrainingtolookpastthesophisticationwithwhichoptimiz

3、ationtheoryisusuallypresentedandrecognizethepracticalsignificanceoftheresults.Thisbookisanattempttopresentalogicaldevelopmentofoptimizationtheoryatanelementarymathematicallevel,withapplicationstosimplebuttypicalprocessdesignandcontrolsituations.Thebookfollowsratherclosely

4、acourseinoptimizationwhichIhavetaughtattheUniversityofDelawaresince1965toclassesmadeupofgraduatestudentsandextensionstudentsfromlocalindustry,togetherwithsomeseniors.Approximatelyhalfofthestudentseachyearhavebeenchemicalengineers,withtheremaindermadeupofothertypesofengine

5、ers,statisticians,andcomputerscientists.TheonlyformalviirillPREFACEmathematicalprerequisitesareafamiliaritywithcalculusthroughTaylorseriesandafirstcourseinordinarydifferentialequations,togetherwiththematurityandproblemawarenessexpectedofstudentsatthislevel.Intwosectionsof

6、Chapter3andinChapter11afamiliaritywithpartialdifferentialequationsishelpfulbutnotessential.Withthisback-grounditispossibletoproceedinonesemesterfromthebasicelementsofoptimizationtoanintroductiontothatcurrentresearchwhichisofdirectprocesssignificance.Thebookdeviatesfromthe

7、courseincontainingmorematerialofanadvancednaturethancanbereasonablycoveredinonesemester,andinthatsenseitmaybelookeduponascomprisinginpartaresearchmonograph.Chapter1presentstheessentialfeaturesofthevariationalapproachwithinthelimitedcontextofproblemsinwhichonlyoneorafinite

8、num-berofdiscretevariablesisrequiredforoptimization.Someofthismaterialisfamiliar,andanumberofint