Mathematicsisplayinganevermoreimportantroleinthephysicaland biologicalsciences,provokingablurringofboundariesbetweenscientific disciplinesandaresurgenceofinterestinthemodernaswellastheclassical techniquesofappliedmathematics. Thisrenewalofinterest,bothin- searchandteaching,hasledtotheestablishmentoftheseriesTextsin AppliedMathematics(TAM). Thedevelopmentofnewcoursesisanaturalconsequenceofahighlevel ofexcitementontheresearchfrontierasnewertechniques,suchasnume- calandsymboliccomputersystems,dynamicalsystems,andchaos,mix withandreinforcethetraditionalmethodsofappliedmathematics. Thus, thepurposeofthistextbookseriesistomeetthecurrentandfutureneeds oftheseadvancesandtoencouragetheteachingofnewcourses. TAMwillpublishtextbookssuitableforuseinadvancedundergraduate andbeginninggraduatecourses,andwillcomplementtheAppliedMat- maticalSciences(AMS)series,whichwillfocusonadvancedtextbooksand research-levelmonographs. Pasadena,California J. E. Marsden Providence,RhodeIsland L.

Sirovich CollegePark,Maryland S. S. Antman Preface This book should serve as an undergraduate text to introduce students of s- ence and engineering to the fascinating ?eld of optimization. Several features have been united: conciseness and completeness, brevity and clarity, emphasis on the justi'cation of ideas and techniques and also on applications, etc. One of the novelties of the text is that it ties together ?elds that are often treated as separate. Indeed, it is hard to ?nd a single textbook where mathematical p- gramming, variational problems, and optimal control problems are explained and integrated as a unity. Thus, our readers may gain an overall view of all aspects of optimization. It is also true that each of the chapters is but a timid introduction to such broad subjects as linear programming, nonlinear programming, numerical op- mizationalgorithms,variationalproblems,dynamicprogramming,andoptimal control.

As a primer in optimization, our aim with this text is no more than to provide a succinct introduction to those worlds, presented in a single resource reference. Thistextcannotanddoesnotpretendtosubstituteintheleastother vii viii Preface moreprofoundtextbooksonthosesub'eldsofoptimization. Readerswithsome experience in optimization seeking a more specialized source in some of those parts will have to look for other references. Real-world applications are also far from this introduction to the subject.