I am about to start writing my next computer program, one which numerically finds the minimum of a function, F, of several variables.
(i.e., -F should be a maximum, and is a function of x1, x2, x3, x4, etc.)
It will be a translation of the NETLIB FORTRAN routine UNCMD.
I am here to ask for advice regarding the most popular problems tackled by such a routine.
Since I cannot write a parser that accepts input of ANY combination of functions, I thought I would post here and ask members their opinions about what they think are the most popular problems solved by multi-dimensional optimization routines. Are they Quadratic Programming problems? Linear Programming problems? Non-linear Least-Squares data-fitting? etc.?
Do you remember any courses from university in which the same type of problem was included every year? Do certain industries use optimization routines to solve the same type of problem all the time?
Your advice and suggestions are welcome.