Including function with design variable as a nonlinear constraint for optimization

I want to minimize "Cost" while "a, b, c" are the variables.

F1 = (1/a) + b

F2 = 2/F1

F3 = F2*3/c

Cost = F1 + F3

One constraint that I have here is

F3 <= 10

I was wondering how can I include the non-linear constraint in fmincon or ga? Any lead will be greatly appreciated.

Answer 1

[Ameer Hamza]

Answered here in comment to your other question: https://www.mathworks.com/matlabcentral/answers/519669-how-to-define-objective-function-that-is-not-a-direct-function-of-decision-variable#comment_832686

F1 = @(a,b,c) (1./a) + b;
F2 = @(a,b,c) 2./F1(a,b,c);
F3 = @(a,b,c) F2(a,b,c).*3./c;
Cost = @(a,b,c) F2(a,b,c) + F3(a,b,c);

lb = [0 0 0]; % lower bounds on a, b, and c
ub = [1 1 1]; % lower bounds on a, b, and c
x0 = rand(1,3); % initial guess

x_sol = fmincon(@(x) Cost(x(1), x(2), x(3)), x0, [], [], [], [], lb, ub, @(x) cons(x, F2));
a_sol = x_sol(1);
b_sol = x_sol(2);
c_sol = x_sol(3);

function [c, ceq] = cons(x, F2)
    ceq = [];
    c = F2(x(1), x(2), x(3)) - 10;
end

Solution:

>> x_sol
x_sol =
    0.0000    0.7288    0.8549

Verify of constraint is met:

    >> F2(x_sol(1), x_sol(2), x_sol(3))
ans =
   4.4348e-09