# fmincon using only gradient vector, without scalar function

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Hailemariam on 27 Sep 2020
Commented: Walter Roberson on 1 Oct 2020
I would like to use MATLAB function fmincon using the gradient vector alone (without scalar function f). But I have trouble with it. For instance, I have tried the following, but it doesn't work. Any help please? Thanks in advance!
x0 = [-1,2];
A = [];
b = [];
Aeq = [];
beq = [];
lb = [-2,-2];
ub = [2,2];
x = fmincon(@myfun,x0,A,b,Aeq,beq,lb,ub)
200*(x(2)-x(1)^2)];
end

#### 1 Comment

Ameer Hamza on 27 Sep 2020
The concept of optimization problem does not make sense without an objective function. What does the gradient even mean in that case? Can you tell me what you are trying to do here?

Walter Roberson on 27 Sep 2020
That is not supported by fmincon. You must return a scalar value as the first output.
If you have set the appropriate option in the option structure, you can also return the gradient as the second output.

Walter Roberson on 27 Sep 2020
The functions with that gradient are
100*X^4 + X^2 - 2*X + 100*Y^2 - 200*X^2*Y + c
for all finite constants c.
The value of c will not change the location of the minima, so you might as well use 0.
Hailemariam on 28 Sep 2020
Thanks. But my plan was to get the solution without the objective function (only using the gradient vector). For instance, if the gradient vector is lager in size, converting into the original function may be challenging (it may take more computational time).
Walter Roberson on 1 Oct 2020
fmincon does not support that. As far as I recall, none of the Mathworks minimizers support that.