Hi
Thank you for reading this question!
I am studying "Fmincon" in Matlab. Based on "Fmincon" document, I wrote a code, as shown below.
fun = @(x)100*(x(2)-x(1)^2)^2 + (1-x(1))^2;
x0 = [-1, 2; -1, 2; -1, 2]';
Aeq = [0.5, 0.1, 0, 0, 0, 0; 0, 0, 2, 1, 0, 0; 0, 0, 0, 0, 0.2, 2];
[x,fval] = fmincon(fun,x0,[],[],Aeq,beq)
Local minimum found that satisfies the constraints.
Optimization completed because the objective function is non-decreasing in
feasible directions, to within the value of the optimality tolerance,
and constraints are satisfied to within the value of the constraint tolerance.
x =
1.5310 -0.6000 -1.1386
2.3448 2.2000 0.6139
In this code, x0 contains six elements. Then, Aeq needs six columns of elements. Based on "Fmincon" document, Equality constraint equation can be written as below:
0.5*x(1)+0.1*x(2)+x(3)+x(4)+x(5)+x(6)=1 (1)
x(1)+x(2)+2*x(3)+x(4)+x(5)+x(6)=1 (2)
x(1)+x(2)+x(3)+x(4)+0.2*x(5)+2*x(6)=1 (3)
In fact, objective function only includes two variables that are x(1) and x(2). Therefore, how does this code ("Fmincon") work? I have not found the similar question in the community. Could anyone explain it or share the relevant link?
Many thanks in advance!
