Running into issue using fsolve

Trying to solve a problem while using fsolve and fmincon. I am getting correct values, but the solvers are running into a large amount of issues. Getting the following error message:

"Warning: Trust-region-dogleg algorithim of FSOLVE cannot handle non-square systems; using Levenberg-Marquardt algorithim instead."

and

"fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance."

Here is my code:

% solve the optimization problem here
options = optimoptions('fmincon','Algorithm','sqp'); % use SQP algorithm
A = []; % linear inequality constraints - NONE
b = []; % NONE
Aeq = []; % linear equality constraints - NONE
beq = []; % NONE
lb = [0.36, 0.05]; % lower bounds on x
ub = [0.44, 0.06]; % upper bounds on x
f=@(p)obj(p,yData);% objective function
nonlcon=[];
p0 = [0.4,0.055];% initial guess from previous problems
[p,fval,exitflag,output,lambda] = fmincon(f,p0,A,b,Aeq,beq,lb,ub,nonlcon,options);

idata = length(yData);
yModel = zeros(idata,1);
for i = 1:idata
    F1 = yData(i,1);
    x = [0.33; yData(i,2); 0.33; F1];
    x = fsolve(@(x)model(x, F1, p),x);
    yModel(i) = x(2);
end

function f = obj(p,yData)
% implement your objective function here - using least-squares method
% p are uncertain model parameters (optimization variables)
% yData is the matrix of experimental data (inputs & outputs)
idata = length(yData);
yModel = zeros(idata,1);
options2 = optimoptions(@fsolve,'Display','off');
for i = 1:idata
    F1 = yData(i,1);
    x0 = [0.33; 0.33; 0.33; F1];
    in = @(x)model(x, F1, p);
    out = fsolve(in, x0, options2);
    yModel(i) = out(2);
end

f = norm(yData(:,2) - yModel)^2;

end

function h = model(x, F1, p)
% Implement the constraints that define the model
k1 = p(1);
k2 = p(2);
Va = 0.08937;
Vb = 0.1018;
Vc = 0.113;
Ya0 = 1;
Yb0 = 0;
Yc0 = 0;
V = 10;

r1 = (k1*x(1))/(x(1)*Va + x(2)*Vb + x(3)*Vc);
r2 = (k2*x(2))/(x(1)*Va + x(2)*Vb + x(3)*Vc);

h = zeros(1:4); 
h(1) = x(1)*x(4) + V*r1 - F1;
h(2) = x(2)*x(4) + V*(r2 - r1);
h(3) = x(3)*x(4) - V*r2;
h(4) = x(1) + x(2) + x(3) - 1; 
end

Any help is greatly appreciated!

[Justyn Welsh]

Just to add, the fmincon was not an error, but showing it is satsfied. Issue is that it seems to be using Levenberg-Maarquardt rather than SQP.

Answer 1

[Matt J]

There are no errors in what you've shown, but it is peculiar that you have one optimization (with fsolve) nested inside another optimization (with fmincon). It would probably be more robust to combine them into one problem, by converting the fsolve equations to fmincon nonlinear equality constraints.

[Justyn Welsh]

Thank you for the input Matt. It is a bit strange, the exercise is dictating for that particular method, but I agree with you.

[Matt J]

You're welcome, but if your question is resolved, please Accept-click the answer.