Suppose I have a fmincon function. As we know from matlab documentation we can impose linear and nonlinear constraints.
Suppose now I have a function of 3 parameters to optimize. And I want 3 of them to be greater than 0 and 1 of them to be greater than -1 I would need 4 constraints but I get an error.
Simple example (working code):
A=eye(4)
A(4,4)=-1;
b=100*ones(4,1)
b(4,1)=+1
fun = @(x)100*(x(2)-x(1)^2)^2 + (1-x(1))^2+x(3);
fmincon(fun,[0,0,0],A,b)
The error is
Error using fmincon (line 287) A must have 3 column(s).
It is strange that A can only have n constraints (that you could add with non linear)
Thanks
Your function fun expects exactly three inputs, i.e. the vector x will always be 3x1. So your starting point must be a 3x1 vector, not 4x1. The fmincon function allows you to specify any number of linear constraints of the form Ax ≤ b. Here, the Ax is a matrix multiplication: each column in A corresponds to one of the dimensions of x, thus A has to have exactly three columns. The number of rows can be any arbitrary number - though of course b will have to have the same dimension!
Small example: if you have the inequality 3*x + 4*y - z ≤ 1, then the first row of A is [3, 4, -1]. And the first entry of b is 1. Now, let's make up an additional constraint, e.g. y ≤ 4, so you have to add a row [0, 1, 0] to A and 4 to b. Your matrices are
A = [3, 4, -1;
0, 1, 0];
b = [1; 4];
In your case, you want more conditions than variables. You can do that by calling eye with two parameters: number of rows and number of columns:
>> A = eye(4, 3);
A =
1 0 0
0 1 0
0 0 1
0 0 0
and manually add the last constraint:
A(4,:) = [0, 0, -1];
To implement the constraint, that all parameters have to be greater than 0, and z has to be smaller than 1, you can create your matrices as follows:
A = -eye(4, 3);
A(4,:) = [0, 0, 1];
b = [zeros(3,1); 1];
i.e. the equations are:
-1 * x ≤ 0, which equals x ≥ 0
-1 * y ≤ 0, which equals y ≥ 0
-1 * z ≤ 0, which equals z ≥ 0
z ≤ 1
now, you can use fmincon:
>>fmincon(fun, zeros(3,1), A, b);
ans =
1.0000
1.0000
0.0000