There's more than 20 functions having to do with minimization
MinMax, ConstrainedMin, NMinimize, NArgMin, FindMinimumCut, NMinValue, MinLimit, Minimize, DiscreteMinLimit, MinValue, ArgMin, FindMinimum, BooleanMinterms, FindMinValue, RankedMin, FindArgMin, MinimalBy, Min, BooleanMinimize, BayesianMinimization, MinDate What is each of them for? Are there patterns to help remember them?
Looking at Names["*Min*"], we find all functions that involve "Min" in their name.
These symbols have to do with finding local and global minima for functions (i.e. $f:\mathbb R\to\mathbb R$)
FindArgMin, NArgMin, ArgMin, (*gives argument(s) of minimum*) FindMinimum, NMinimize, Minimize, (*gives list(s) {arg,value}*) FindMinValue, NMinValue, MinValue (*gives value(s) of minimum*) The middle row is all that really matters
Find*Min is numerical, and iteratively steps toward a local min from a starting point.N*Min is semi-numerical, and looks for a global min.Min gives the smallest value of a listRankedMin gives the $n$th smallest value of a listMinimalBy allows the use of a function to evaluate smallness. Since different elements could evaluate to the same number, it returns all minimal elements instead of just oneThere are other functions that have to do with minimizing on different pieces of data, like booleans, graphs, colors, dates, sequences, etc.
For each of the functions, there's a maximization counterpart (except MinMax which is just {Min@#,Max@#}&).
The functions aren't named perfectly: Minimize being related to MinValue but not to Min is annoying.