# Thread: Multi-dimensional Numerical Optimization Program

1. ## Multi-dimensional Numerical Optimization Program

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?

2. ## Re: Multi-dimensional Numerical Optimization Program

Hey DavidB.

Optimization is an area of applied mathematics [in its own right now] and there are a number of theoretical and applied sub-areas of the discipline to "explore".

I'd take a look at any book [or lecture resources] in that area and then "branch out" for more information.

3. ## Re: Multi-dimensional Numerical Optimization Program

Thanks for the feedback, chiro.

I am planning to turn the program into a JavaScript webpage later, and would like to pick sample problems that are the most widely applicable. Maybe something like the following:

A x^2 + B y^2 + C z^2 + D xy + E yz + F xz

That way, a user has the freedom to enter values for A, B, C, D, E, and F, but I don't have to write specific programs for several different problems.

I plan to later modify the program to perform non-linear least squares data-fitting.
I have some data that looks very close to a modified sech or cosh function and would like to see what the best fit is. Once I get my own program working, I'll probably post back here asking if other users could test the data too, to verify my results.

4. ## Re: Multi-dimensional Numerical Optimization Program

I am about to start writing my next computer program

...What was the last one about?