Objective Function for Symmetrical Solution with fmincon?

Hello,

I am writing a code that uses fmcinon to solve for the solution of a system that is constrained by various linear and nonlinear equality constraints (no inequality constraints). In addition to finding the solution that provides the smallest f(x), I would also like to create an objective function that will find the most symmetrical solution. By symmetrical, I mean that the values inside x are as close to one another as possible.

Here's a few ideas I've been playing with.

1) f = sum(x^2)

2) f = sum(x^2) / length(x)

3) xAverage = sum(x) / length(x)
   cost = sum((x - xAvg).^2) / length(x)

Any thoughts or suggestions? Thanks!

Answer 1

[Matt J]

You can try adding a penalty on the variance or the first differences in x,

1. min. f(x)+beta*var(x)
2. min. f(x)+beta*norm(diff(x))^2

where beta>0 is a weight factor on the penalty term controlling its priority level.