How to implement inequality constrainst in fmincon

Hi, I need to implement inequality constraint for fmincon. The constraint is Z < d where d is constant and Z is function https://www.mathworks.com/matlabcentral/answers/388799-how-to-implement-inequality-constrainst-in-fmincon#imageof optimization variable x. Z is given as max(W*f(x)), here f(x) is linear and given f(x) = mx+c and W is a constant matrix. I have written following code for this function but do not know how to adapt it for fmincon. Secondly, is there a way to invert this function so that it can be written as bound constraint instead of inequality. Any help would be appreciated.

    d = 3;
    W = [1, 0.5, 0.25; 0, 1, 0.5; 0, 0, 1]; 
    x = rand(3,3);
    fx = 0.7*x + 0.5; 
    P = W*fx; 
    Z = max(P);
    Z = Z - d;

Answer 1

[vijaya lakshmi]

Hi Saifullah Khalid ,

In order to adapt the inequality constraint in fmincon, you can take advantage of the additional input parameter to “fmincon” called ‘nonlcon’.

The purpose of ‘nonlcon’ is to allow you to implement a function that takes in the vector input and add constraints to an output array.

For further information about ‘nonlcon’, please see the Input Arguments > nonlcon section in the following documentation: fmincon

To add the additional constraints to "fmincon", create an additional function that will be used to specify constraints. Add this function handle to the call to "fmincon"

Refer to the below example to understand its usage:

   fmincon(@(m0)myfunc(m0, other_params), m0, [], [], [], [], LB, UB) ; %fmincon

Where m0 is the initial estimate for m.

fmincon(@(m0)myfunc(m0, other_params), m0, [], [], [], [], LB, UB, @constrainM) %fmincon with function handle added

function [c, ceq] = constrainM(m0) % inequality constraint function

[Saifullah Khalid]

Vijay thanks,