Algorithms for Minimization Without Derivatives

Thisoutstandingtextforgraduatestudentsandresearchersproposesimprovementstoexistingalgorithms,extendstheirrelatedmathematicaltheories,andoffersdetailsonnewalgorithmsforapproximatinglocalandglobalminima.Noneofthealgorithmsrequiresanevaluationofderivatives;alldependentirelyonsequentialfunctionevaluation,ahighlypracticalscenariointhefrequenteventofdifficult-to-evaluatederivatives.Topicsincludetheuseofsuccessiveinterpolationforfindingsimplezerosofafunctionanditsderivatives;analgorithmwithguaranteedconvergenceforfindingaminimumofafunctionofonevariation;globalminimizationgivenanupperboundonthesecondderivative;andanewalgorithmforminimizingafunctionofseveralvariableswithoutcalculatingderivatives.Manynumericalexamplesaugmentthetext,alongwithacompleteanalysisofrateofconvergenceformostalgorithmsanderrorboundsthatallowfortheeffectofroundingerrors.