Optimizationtechniquesareatthecoreofdatascience,includingdataanalysisandmachinelearning.Anunderstandingofbasicoptimizationtechniquesandtheirfundamentalpropertiesprovidesimportantgroundingforstudents,researchers,andpractitionersintheseareas.Thistextcoversthefundamentalsofoptimizationalgorithmsinacompact,self-containedway,focusingonthetechniquesmostrelevanttodatascience.Anintroductorychapterdemonstratesthatmanystandardproblemsindatasciencecanbeformulatedasoptimizationproblems.Next,manyfundamentalmethodsinoptimizationaredescribedandanalyzed,including:gradientandacceleratedgradientmethodsforunconstrainedoptimizationofsmooth(especiallyconvex)functions;thestochasticgradientmethod,aworkhorsealgorithminmachinelearning;thecoordinatedescentapproach;severalkeyalgorithmsforconstrainedoptimizationproblems;algorithmsforminimizingnonsmoothfunctionsarisingindatascience;foundationsoftheanalysisofnonsmoothfunctionsandoptimizationduality;andtheback-propagationapproach,relevanttoneuralnetworks.
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