# How to correctly specify fmincon nonlinear constraints

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Christopher on 8 Apr 2020
Commented: Christopher on 9 Apr 2020
Since the fmincon cin(x) and ceq(x) nonlinear function constraints have to return vectors, what happens when thse functions return a scalar value? Is the scalar used to create a correctly sized vector filled with the scalar value? See example code below:
function [cin, ceq] = nonlcon(x)
cin = -1;
ceq = x'*H*x - sd.^2; % where H and sd are global.
end

#### 1 Comment

Matt J on 8 Apr 2020
Note that this constraint
cin = -1;
is independent of x, as you have written it. It corresponds to the inequality -1<=0, which is always satisfied independently of x.

Matt J on 8 Apr 2020
Edited: Matt J on 8 Apr 2020
The lengths of the vectors cin and ceq tell fmincon how many inequality and equality constraints you have. So, if they are scalars (i.e., vectors of length 1) then fmincon will assume that you have only 1 inequality and equality constraint. Moreover, those constraints will be considered satisfied if and only if x results in cin<=0 and ceq==0 (up to the ConstraintTolerance parameter you have set).

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Matt J on 8 Apr 2020
And a scalar is a vector (of length 1), so nothing in the documentation is violated if you return scalar-valued cin and ceq.
Matt J on 8 Apr 2020
Maybe it will help to point out that the lengths of x, cin, and ceq are all unrelated to one another. The length of cin is simply the number of nonlinear inequality constraints that you have, and analogously for ceq. There is no link between the number of any of the constraints and length(x).
Christopher on 9 Apr 2020
Got it and thanks for the clarification, it is much appreciated...