I recently wrote a simple particle filter for a robotics project and needed an arg_min function.  This function returns the argument that results in a minimum value of a function (as opposed to the minimum argument value itself https://en.wikipedia.org/wiki/Arg_max). In my case, from a list of points I needed to find the point that was closest to another given point. 

I based my implementation on the examples given on cppreference for std::transform and std::min_element.  The major advantage of a combined algorithm as opposed to using std::transform and std::min_element individually is that it cuts the number of function evaluations in half by caching the result. A working implementation for arg_min is here: https://godbolt.org/z/P58Yca.  Arg_max is similar and overloads to eliminate the begin/end iterators could be added (and probably ones to work with ranges, although I have no experience with them yet).

I think this would be a valuable addition to the algorithms library as it has fairly broad applicability. I'm curious what others think.