fmincon implementing nonlinear constraints

I am trying to fit my objective function (ogden_funct) to the following constraints and am running into errors.

For constraint 1) I get an error of 'Error using fmincon

Supplied objective function must return a scalar value'

For constraint 2) I am not sure where/how to implement this.

My ideal solution will implement constraint 1) and 2)

Any ideas help.

%objective 
    ogden_funct = @(c) c(1)*(xdata.^(c(4)-1)-xdata.^((-1)/2*c(4)-1)) + ...
    c(2)*(xdata.^(c(5)-1)-xdata.^(-1/2*c(5)-1)) + ...
    c(3)*(xdata.^(c(6)-1)-xdata.^((-1)/2*c(6)-1))- ydata;


% Constraint 1)
c(1)*c(4) + c(2)*c(5) + c(3)*c(6) = 2;

% my attempt, writing a function nlcon(c) in a new file

function [z, zeq] = nlcon(c)
    z = 2 - (c(1)*c(4) + c(2)*c(5) + c(3)*c(6));
    zeq = [];
    
end    




% then calling fmincon
    x = fmincon(ogden_funct, Initial_Guess,A,b,Aeq,beq,[],[],nonlincon);  % Where Initial_Guess...[] in this case dont matter
    
    
    
% Constraint 2)
    c(1)*c(4)>0; c(2)*c(5)>0; c(3)*c(6)>0; % no ideas on how to implement this
    
    

[Torsten]

Objective for fmincon must be

ogden_funct = @(c) sum(c(1)*(xdata.^(c(4)-1)-xdata.^((-1)/2*c(4)-1)) + ...
    c(2)*(xdata.^(c(5)-1)-xdata.^(-1/2*c(5)-1)) + ...
    c(3)*(xdata.^(c(6)-1)-xdata.^((-1)/2*c(6)-1))- ydata).^2;

Constraints are

function [z, zeq] = nonlincon(c)
zeq = 2 - (c(1)*c(4) + c(2)*c(5) + c(3)*c(6));
z = [-c(1)*c(4),-c(2)*c(5),-c(3)*c(6)];   
end  

c(1)*c(4)>0; c(2)*c(5)>0; c(3)*c(6)>0 is hard to archieve - try >=0 instead.

[Walter Roberson]

c(1)*c(4)>0

You are probably not going to be able to achieve that with fmincon(). It creates discontinuous regions, c1 and c4 both positive or c1 and c4 both negative. fmincon() cannot support discontinuous regions like that.

[Reed]

Okay, I really appreciate that. Could you describe to me, in the function script, what the z = [.....] is achieving? I really appreciate your answer @Torsten

[Matt J]

Objective for fmincon must be ogden_funct = @(c) sum(c(1)*(xdata.^(c(4)-1)....).^2;

mean() would be better:

ogden_funct = @(c) mean(c(1)*(xdata.^(c(4)-1)-xdata.^((-1)/2*c(4)-1)) + ...
    c(2)*(xdata.^(c(5)-1)-xdata.^(-1/2*c(5)-1)) + ...
    c(3)*(xdata.^(c(6)-1)-xdata.^((-1)/2*c(6)-1))- ydata).^2;

That way, your optimoptions needn't depend so much on the size of xdata.

[Torsten]

@Reed

Could you describe to me, in the function script, what the z = [.....] is achieving?

It's an attempt to implement your constraints

-c(1)*c(4) <= 0
-c(2)*c(5) <= 0
-c(3)*c(6) <= 0