How to set constraints for outpus of objective function in fmincon

Hi, I am new in optimization. I am implementing an algorithm, where inside the optimization function the values of three varaibles are with in certain range, which are set as constraints. how it can be done?

[John D'Errico]

There is not need to set explicit constraints on the variables. Fmincon allows you to specify bounds on the variables. Why does this not do what you ask for?

[Raihan Ul Islam]

i have three variables like x1, x2, x3 inside objective function. From these three values a single value is computed which is output of objective function. But there should be some constraints

1. 0>=Xi>=1 ; i=1,2,3,
2. x3>x2>x1.

How can i enforce the above two constraints. Usually objective function gets values of other variables from fmincon. Here i have to check if the values are following above constraints.

Answer 1

[John D'Errico]

If x1,x2,x3 are optimization parameters, then it is simple.

Case 1 is simply a set of bound constraints. As I said, fmincon explicitly allows upper and lower bound constraints.

Case 2 is a set of TWO linear inequality constraints. Again, fmincon allows linear inequalities, although essentially no optimizer will allow strict inequality constraints. You need to formulate it in the form of

x(3) >= x(2) 
x(2) >= x(1)

If you insist on strict inequality constraints, then I suggest using an offset tolerance. Thus

x(3) >= x(2) + mytol
x(2) >= x(1) + mytol

where you set mytol to be some reasonably small positive number.

Again, these are simple linear inequalities, a facility that is explicitly allowed using fmincon. READ THE HELP FOR FMINCON.

If you mean that x1,x2,x3 are computed inside your objective function, then you will need to supply a nonlinear constraint function that computes them independently. Again, this is a facility that is supported by fmincon.

Best of course is if you write one external function that can compute these values. Then you need write the code only once.

Yes, I know that you will next complain that then you will need to compute those parameters twice, once in your objective, and once in your constraint function. WRONG! MATLAB now has a memoization tool that can remember if a function has been called with a given set of parameters, and not need to recompute the values.

help memoize