Getting the "Error running optimization. Too many output arguments." when running fmincon with gradient option in derivatives.

Hi,

I'm trying to optimize a problem of engine performance using a external function 'finter' (external deck - executable). That function works properly as I have checked it many times.

My objective function is as follows:

function [m]=fobjetivo(X)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%% Function to calculate the Obj Func  %%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Tt41 = 1350;
Tt42 = 1500;
[y1] = finter(X,Tt41);
[y2] = finter(X,Tt42);
ys1 = [-1.60742937984057;-1.75941194993574;-1.52016066840023;-1.38821355190586;-1.26737524545974;-1.11748814435432;-0.968998107063983;-1.31351767471495;-1.48990020304618;-1.29056672044894];
ys2 = [-0.218867980285718;-0.146046874197578;-0.0918019106772645;-0.0117144187008822;0.101770383589507;0.238687435338204;0.389060531152024;0.0547756208261101;-0.0687671839852227;0.0390575624990874];
m = sqrt(((norm(y1-ys1))^2)+((norm(y2-ys2))^2));
end

I have only as constraints the following conditions:

a) The solution must count with all the components (the solution X counts with 10 components) in between 0 and 2. That's whay my UB and LB are as follows:

LB = [0;0;0;0;0;0;0;0;0;0]
UB = [2;2;2;2;2;2;2;2;2;2]

b) The components must be positive always. That's why my non-linear constraint function is as follows:

function [c,ceq] = nonlcon(x)
       c=-prod(x) ; 
    ceq= []; 
end

The initial point I use for the iterations is the following:

X0 = [0.0650000000000000; 1.12240000000000; 1.76370000000000; 1.33840000000000; 0.380900000000000; 0.737800000000000; 1.96330000000000; 1.96330000000000; 0.312800000000000; 1.71100000000000]

It is interesting that, when I select the option "approximate by solver" in the derivatives, the tool starts the optimization. Finally it says that the initial point given is a good solution:

Objective function value: 1.6591997092884727

Initial point is a local minimum that satisfies the constraints.

Optimization completed because at the initial point, 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.

Obviously, that is not a valid answer because I know the solution of the problem is as follows:

Xsolv = [0.602900000000000; 1.40220000000000; 1.33270000000000; 1.07830000000000; 1.39620000000000; 1.33310000000000; 0.356300000000000; 0.256000000000000; 1.99820000000000; 0.342200000000000]

But, at least, the progam starts doing something.

With the "gradient" option in the derivatives the tool finds this problem:

Error running optimization.

Too many output arguments.

Any idea on where the issue may be?

My problem is quite dependant on the function. I know that some colleague has used the gradient succesfully in this very same problem and, frankly speaking, it seems the SQP-gradient seems to be the right approach here, but 'm not capable to make it work so far.

Thanks,

JRR

[Matt J]

b) The components must be positive always. That's why my non-linear constraint function is as follows:

That is already ensured by

LB = [0;0;0;0;0;0;0;0;0;0]

Also, prod(x)>=0 does not ensure that all componets are greater than zero, for example, x=-ones(1,10) satisfies the constraints but none of its elements are positive.

[Walter Roberson]

For strictly positive, use LB of all eps(realmin) [and no nonlinear constraint.]

Answer 1

[Matt J]

Any idea on where the issue may be?

It sounds like you have set SpecifyObjectiveGradient=true. However, it does not appear from your code that you have fobjetivo(X) performs any gradient calculation.

[José Rodrigo Ramírez]

Hi Matt,

I was using the optimization tool. It generated the following code:

function [x,fval,exitflag,output,lambda,grad,hessian] = code case(x0,lb,ub)
%% This is an auto generated MATLAB file from Optimization Tool.

%% Start with the default options
options = optimoptions('fmincon');
%% Modify options setting
options = optimoptions(options,'Display', 'off');
options = optimoptions(options,'Algorithm', 'sqp');
options = optimoptions(options,'SpecifyConstraintGradient', true);
options = optimoptions(options,'SpecifyObjectiveGradient', true);
[x,fval,exitflag,output,lambda,grad,hessian] = ...
fmincon(@fobjetivo,x0,[],[],[],[],lb,ub,@nonlcon,options);

Best regards,

JRR

[Matt J]

Yes, but when SpecifyConstraintGradient and/or SpecifyObjectiveGradient are set true, you are responsible for supplying the appropriate code for the gradient computations.

https://www.mathworks.com/help/optim/ug/fmincon.html#busxd7j-1

https://www.mathworks.com/help/optim/ug/optimization-toolbox-tutorial.html#tutdemo-6

[José Rodrigo Ramírez]

ok, that makes sense.

I will explore that.

Thanks Matt,

José

[Matt J]

You're welcome, but please Accept-click the answer if it gets you to a solution.