MATLAB: ERROR: FMINCON requires all values returned by functions to be of data type double.

Question

I have this function evalQ_test:

function Q = evalQ_test(x)
%%%

%%% Q_1 = x(1)+x(2);
%%%
Q=double(-(Q_1+Q_2+Q_3));
end

I omitted most of what the real content of the function here by %%%.

Following https://www.mathworks.com/help/optim/ug/writing-scalar-objective-functions.html,

I have this objective function:

function [f, g, H] = evalQ_1(x)
% Calculate objective f
f = @(x) evalQ_test(x);
 
if nargout > 1 % gradient required
    g = [f([x(1)+delta;x(2)])-f([x(1);x(2)]);f([x(1);x(2)+delta])-f([x(1);x(2)])];
    
    if nargout > 2 % Hessian required
        H = [x(1),0;0,x(2)];
    end
end

And Hessian function:

function Hout = hessianfcn(x,lambda)
delta = 10^(-6);
% Hessian of objective
    H = [x(1),0;0,x(2)];
% Hessian of nonlinear inequality constraint
Hg = 2*eye(2);
Hout = H + lambda.ineqnonlin*Hg;

Suppose the gradient and hessian are calaulated correctly here.

Then I run:

fun = @evalQ_1;
x0 = [1;1];
options = optimoptions('fmincon','Algorithm','interior-point',...
'SpecifyObjectiveGradient',true,'SpecifyConstraintGradient',true,...
'HessianFcn',@hessianfcn);
[x,fval,exitflag,output] = fmincon(fun,x0,[],[],[],[],[],[],[],options);

However, I have the error:

"Error using fmincon (line 694)

FMINCON requires all values returned by functions to be of data type double."

Is it because I am using a nested objective function? Or anything else?

Thanks in advance!!

Answer 1

Your objective function evalQ_1 is returning a function handle

f = @(x) evalQ_test(x);

whereas fmincon expect the first output to be a numeric value. Try something like this

function [f_, g, H] = evalQ_1(x)
% Calculate objective f
f = @(x) evalQ_test(x);
f_ = f(x);
 
if nargout > 1 % gradient required
    g = [f([x(1)+delta;x(2)])-f([x(1);x(2)]);f([x(1);x(2)+delta])-f([x(1);x(2)])];
    
    if nargout > 2 % Hessian required
        H = [x(1),0;0,x(2)];
    end
end