Algorithms for Optimization

Thisbookoffersacomprehensiveintroductiontooptimizationwithafocusonpracticalalgorithms.Thebookapproachesoptimizationfromanengineeringperspective,wheretheobjectiveistodesignasystemthatoptimizesasetofmetricssubjecttoconstraints.Readerswilllearnaboutcomputationalapproachesforarangeofchallenges,includingsearchinghigh-dimensionalspaces,handlingproblemswheretherearemultiplecompetingobjectives,andaccommodatinguncertaintyinthemetrics.Figures,examples,andexercisesconveytheintuitionbehindthemathematicalapproaches.ThetextprovidesconcreteimplementationsintheJuliaprogramminglanguage.Topicscoveredincludederivativesandtheirgeneralizationtomultipledimensions;localdescentandfirst-andsecond-ordermethodsthatinformlocaldescent;stochasticmethods,whichintroducerandomnessintotheoptimizationprocess;linearconstrainedoptimization,whenboththeobjectivefunctionandtheconstraintsarelinear;surrogatemodels,probabilisticsurrogatemodels,andusingprobabilisticsurrogatemodelstoguideoptimization;optimizationunderuncertainty;uncertaintypropagation;expressionoptimization;andmultidisciplinarydesignoptimization.AppendixesofferanintroductiontotheJulialanguage,testfunctionsforevaluatingalgorithmperformance,andmathematicalconceptsusedinthederivationandanalysisoftheoptimizationmethodsdiscussedinthetext.Thebookcanbeusedbyadvancedundergraduatesandgraduatestudentsinmathematics,statistics,computerscience,anyengineeringfield,(includingelectricalengineeringandaerospaceengineering),andoperationsresearch,andasareferenceforprofessionals.