Error using fmincon. Supplied objective function must return a scalar value.

The following is my code. I am getting the error shown at the end. I cannot figure out why its displaying this error.

Please help me understand this error. Ive tried alot of things and none of them work. Thank you!

clc;
clear;
close all;
% x = lhsdesign(20,4);% Run at the beginning screen shot result and don't need that anymore
x=[ 13.5870 248.6600 16.4220 15.8350
    14.1440 231.7500 15.0310 16.6400
    13.7170 233.7000 16.1970 16.9600
    14.0000 241.6100 15.6310 15.2910
    14.2650 236.0400 15.9950 15.0130
    14.6370 237.2000 15.5410 15.5040
    14.3380 235.3300 16.6010 15.1400
    13.4440 234.6400 16.5310 16.1600
    14.8520 247.2200 15.8160 16.7920
    13.0300 232.0800 16.7990 16.2290
    14.5480 246.9800 15.4450 15.7550
    14.4010 242.2100 16.8550 15.9780
    13.2170 245.9800 15.1260 15.3330
    13.3300 244.6100 15.7880 15.6100
    13.9740 249.2500 16.9100 16.0440
    14.7580 230.5200 15.3820 16.5030
    14.9700 239.7100 15.2430 16.4680
    13.8800 240.2600 16.0920 15.4110
    13.1850 238.1100 16.3530 16.3200
    13.6120 243.5500 16.2870 16.8530];
ub = [15 250 17 17];% determine before FEA 
lb = [13 230 15 15];% determine before FEA
x_in = lb+(ub-lb).*x; % Train LHSdesign results so we can control 
% parameters in appropriate range

% x_in(:,1) = lb(1) + (ub(1)-lb(1))*x(:,1);
% x_in(:,2) = lb(2) + (ub(2)-lb(2))*x(:,2);
% x_in(:,3) = lb(3) + (ub(3)-lb(3))*x(:,3);
% x_in(:,4) = lb(4) + (ub(4)-lb(4))*x(:,4);
% Creating Random Y-Vector
Deformation_mm = [2.17 1.468 1.687 1.779 1.520 1.665 1.486 1.867 ...
    1.489 2.017 1.701 1.660 2.387 2.288 1.965 1.260 ...
    1.335 1.860 2.085 1.982]'; % Y_out2
Mass_kg = [1.095 1.0826 1.08058 1.08326 1.08422 1.09308 1.08531 ...
    1.07737 1.09688 1.07289 1.09167 1.09018 1.07647 1.07821 ...
    1.08759 1.08892 1.09446 1.08253 1.07586 1.08255]'; % Y_out2
rho = 0.9;
rbf_coeff1 = rbf(x_in,Deformation_mm,rho,'Multiquadric');
rbf_coeff2 = rbf(x_in,Mass_kg,rho,'Multiquadric');
%rbf_coeff = [rbf_coeff1,rbf_coeff2]
x0 = lb;
Aeq = [];
beq = [];
A = [];
b = [];
options = optimoptions('fmincon','Algorithm','sqp','Display', ...
    'iter-detailed','PlotFcn',@optimplotfval);

k=1; 
for w1 = rbf_coeff1
    w2 = rbf_coeff2;
    
    [xopt3,fopt3] = fmincon(@objfun,x0,A,b,Aeq,beq,lb,ub, ...
        @nonlcon,options,x_in,w1,w2);
    [AOF,f] = objfun(xopt3,1,1);
    f1(k) = f(1);
    f2(k) = f(2);
    
    k = k+1
    fprintf('iter: %d,\t f1: %f,\t f2: %f \n',k,f(1),f(2))
end
plot(f1,f2,'o');
xlabel('f1');
ylabel('f2');

xopt = [xopt1; xopt2]';
fopt = [fopt1 fopt2];
Mass_X = xopt(:,1);
Deformation_X = xopt(:,2);
Mass_F = fopt(:,1);
Deformation_F = fopt(:,2);
Design_Vars = {'Beam Diameter';'Beam Length';'Motor Mnt Height';'Motor Mnt Diameter'};
Set_Number = (1:length(x_in))';
Beam_Diameter = x_in(:,1);
Beam_Length = x_in(:,2);
Motor_Mnt_Height = x_in(:,3);
Motor_Mnt_Diameter = x_in(:,4);
FEA_Results = table(Set_Number, Deformation_mm, Mass_kg)
Optimization_for_X = table(Design_Vars, Mass_X, Deformation_X)
Optimization_for_F = table(Mass_F, Deformation_F)
Surrogate_Training = table(Set_Number,Beam_Diameter,Beam_Length, ...
    Motor_Mnt_Height, Motor_Mnt_Diameter)

function [aof,f] = objfun(x,x_in,rbf_coeff1,rbf_coeff2)
rho=0.9;
f(1) = rbf_approx(x_in,x,rbf_coeff1,rho,'Multiquadric'); % Mass
f(2) = rbf_approx(x_in,x,rbf_coeff2,rho,'Multiquadric'); % Mass
aof = rbf_coeff1*f(1) + rbf_coeff2*f(2);
end
function [c,ceq]=nonlcon(x,x_in,rbf_coeff1, rbf_coeff2)
c(1)=x(1)-5;
c(2)=x(2)-6;
c(3)=x(3)-7;
c(4)=x(4)-8;
% c(5)=x(5)-9;
ceq=[];
end

This is my error:

Error using fmincon (line 640)

Supplied objective function must return a scalar value.

Error in ProjectCode (line 80)

[xopt3,fopt3] = fmincon(@objfun3,x0,A,b,Aeq,beq,lb,ub, ...

Answer 1

[Walter Roberson]

for w1 = rbf_coeff1
    w2 = rbf_coeff2;

That is not a dual "for" loop !! It does not simultaneously iterate through rbf_coeff1 and rbf_coeff2. It does not iterate through all possible pairs of the two, and it does not iterate through "corresponding" values -- the K'th iteration has w1 = rbf_coeff1(K) but will not have w2 = rbf_coeff2(K) .

MATLAB has no "multiple" for loop. Not anywhere.

Instead, your code is iterating over rbf_coeff1 values into w1, but w2 is being set to be all of the vector rbf_coeff2 .

        
    [xopt3,fopt3] = fmincon(@objfun,x0,A,b,Aeq,beq,lb,ub, ...
        @nonlcon,options,x_in,w1,w2);

You are using a syntax that has not been documented in at least 15 years.

In fmincon() and ode*() calls, if you pass in extra parameters after the options, then every call to a user-specified function will have the extra parameters passed in to it. That includes when nonlcon is called -- and it includes when @optimplotfval is called.

Exception: there are some options that need more control parameters than usual, and those control parameters go after the options structure. So in some cases that w1 option would be interpreted as a parameter to some of the work specified by the options. fmincon() and ode*() do not care and will not try to warn you that you might have messed that up: since the ability to pass in extra parameters has not been documented for a long long time, Mathworks considers it to be your fault if something goes wrong when you use it.

You should be parameterizing your function instead: http://www.mathworks.com/help/matlab/math/parameterizing-functions.html

Anyhow... with w2 being the full rbf_coeff2 vector, your code

 aof = rbf_coeff1*f(1) + rbf_coeff2*f(2);

is going to create a vector because rbf_coeff2 is a vector.

[AeroEng]

So i did completely remove the for loop and i am still running into this issue. Any ideas why? I am very confused.

My new code:

clc;
clear;
close all;

x=[   13.5870  248.6600   16.4220   15.8350
      14.1440  231.7500   15.0310   16.6400
      13.7170  233.7000   16.1970   16.9600
      14.0000  241.6100   15.6310   15.2910
      14.2650  236.0400   15.9950   15.0130
      14.6370  237.2000   15.5410   15.5040
      14.3380  235.3300   16.6010   15.1400
      13.4440  234.6400   16.5310   16.1600
      14.8520  247.2200   15.8160   16.7920
      13.0300  232.0800   16.7990   16.2290
      14.5480  246.9800   15.4450   15.7550
      14.4010  242.2100   16.8550   15.9780
      13.2170  245.9800   15.1260   15.3330
      13.3300  244.6100   15.7880   15.6100
      13.9740  249.2500   16.9100   16.0440
      14.7580  230.5200   15.3820   16.5030
      14.9700  239.7100   15.2430   16.4680
      13.8800  240.2600   16.0920   15.4110
      13.1850  238.1100   16.3530   16.3200
      13.6120  243.5500   16.2870   16.8530];
ub = [15 250 17 17];% determine before FEA 
lb = [13 230 15 15];% determine before FEA
x_in = lb+(ub-lb).*x; % Train LHSdesign results so we can control 
                      % parameters in appropriate range

% Creating Random Y-Vector


Deformation_mm = [2.17 1.468 1.687 1.779 1.520 1.665 1.486 1.867  ...
                  1.489 2.017 1.701 1.660 2.387 2.288 1.965 1.260 ...
                  1.335 1.860 2.085 1.982]'; % Y_out2
Mass_kg = [1.095 1.0826 1.08058 1.08326 1.08422 1.09308 1.08531 ...
           1.07737 1.09688 1.07289 1.09167 1.09018 1.07647 1.07821 ...
           1.08759 1.08892 1.09446 1.08253 1.07586 1.08255]'; % Y_out2

rho = 0.9;
rbf_coeff1 = rbf(x_in,Deformation_mm,rho,'Multiquadric');
rbf_coeff2 = rbf(x_in,Mass_kg,rho,'Multiquadric');



x0 = lb;
Aeq = [];
beq = [];
A = [];
b = [];

          
options = optimoptions('fmincon','Algorithm','sqp','Display', ...
                       'iter-detailed','PlotFcn',@optimplotfval);
          


[xopt3,fopt3] = fmincon(@objfun3,x0,A,b,Aeq,beq,lb,ub, ...
                 @nonlcon3,options,x_in,rbf_coeff1,rbf_coeff2);
[AOF,f] = objfun3(xopt3,1,1);

          
xopt = [xopt1; xopt2]';
fopt = [fopt1 fopt2];

Mass_X = xopt(:,1);
Deformation_X = xopt(:,2);
Mass_F = fopt(:,1);
Deformation_F = fopt(:,2);

Design_Vars = {'Beam Diameter';'Beam Length';'Motor Mnt Height';'Motor Mnt Diameter'};
Set_Number = (1:length(x_in))';
Beam_Diameter = x_in(:,1);
Beam_Length = x_in(:,2);
Motor_Mnt_Height = x_in(:,3);
Motor_Mnt_Diameter = x_in(:,4);

FEA_Results = table(Set_Number, Deformation_mm, Mass_kg)
Optimization_for_X = table(Design_Vars, Mass_X, Deformation_X)
Optimization_for_F = table(Mass_F, Deformation_F)
Surrogate_Training = table(Set_Number,Beam_Diameter,Beam_Length, ...
                           Motor_Mnt_Height, Motor_Mnt_Diameter)
                       

function [aof,f] = objfun3(x,x_in,rbf_coeff1,rbf_coeff2)

rho=0.9;
rbf_coeff = [rbf_coeff1 rbf_coeff2];
f(1) = rbf_approx(x_in,x,rbf_coeff(:,1),rho,'Multiquadric'); % Mass
f(2) = rbf_approx(x_in,x,rbf_coeff(:,2),rho,'Multiquadric'); % Mass

aof = rbf_coeff1*f + rbf_coeff2*f;

end


function [c,ceq]=nonlcon3(x,x_in,rbf_coeff1, rbf_coeff2)
c(1)=x(1)-5;
c(2)=x(2)-6;
c(3)=x(3)-7;
c(4)=x(4)-8;

ceq=[];
end

Thank you so much for your help