Many inferences in Statistics, e.g., Maximum Likelihood Estimates, reduce to optimization. However, in MLE optimization is used for number crunching only and has nothing to do with motivation and performance analysis of the estimate. Most of traditional applications of Optimization in Statistics are of similar "number crunching'' nature; they are beyond the scope of the course.
What is in the scope of the course, are inference routines motivated and justified by Optimization Theory (Convex Analysis, Conic Programming, Saddle Points, Duality...), the working horse being convex optimization.
This choice is motivated by
- nice geometry of convex sets, functions, and optimization problems
- computational tractability of convex optimization implying computational efficiency of statistical inferences stemming from Convex Optimization.For more comments on "course's philosophy'' and for detailed description of course's contents, see Preface and Table of Contents in Lecture Notes available at https://www2.isye.gatech.edu/~nemirovs/StatOpt_LN.pdf
