fmincon with a RBF toolbox

I have approximated a function using a RBF toolbox. Now, I woud like to optimize this function using fmincon. However, I do not know how to use the fmincon in this case.

   %Create plot of original function:
  x=(0:0.001:1)';
  y=((6.*x-2).^2).*sin(12.*x-4);
  plot(x,y,'k','LineWidth',2)
  xlabel('x','FontSize',12,'Color','k','FontWeight','bold');
  ylabel('y','FontSize',12,'Color','k','FontWeight','bold');
  hold on

   %Samples:
  Xtr=[0;0.2;0.4;0.6;0.8;1];
  Ytr=[3.0272;-0.6397;0.1148;-0.1494;-4.9491;15.8297];

   %Build the metamodel:
  [model, time] = rbfbuild(Xtr, Ytr,'MQ',1);

   %Plot the approximate function:
  Xq=(0:0.01:1)'; 
  [Yq] = rbfpredict(model, Xtr, Xq);
  plot(Xq,Yq,'--k','LineWidth',2)
  legend('Função original','Função aproximada');
  plot(Xtr,Ytr,'*k','MarkerSize',10);
  hold off

   %Verify quality of metamodel:
  Xtst=[0.1;0.3;0.7;0.9];%Pontos para teste
  Ytst=[-0.6566;-0.0156;-4.6058;5.7120]; 

[MSE, RMSE, RRMSE, R2] = rbftest(model, Xtr, Xtst, Ytst)

   %Optimization:
  LB = [0]; 
  UB= [1]; 
  x=[0.5]; 

A= [];
B= [];
Aeq=[];
Beq=[];

options = optimset('MaxIter',300000000,'MaxFunEvals',100000000);
[x,Yq]=fmincon(rbfpredict(model,Xtr,Xq), x, A,B,Aeq,Beq,LB,UB)

[Rena Berman]

(Answers Dev) Restored edit

Answer 1

[Walter Roberson]

You need to pass a function handle to fmincon . That might look something like,

x0 = rand;
[best_x, Yq] = fmincon( @(x) rbfpredict(model, Xtr, Xq, x), x0, A, B, Aeq, Beq, LB, UB, [], options);

rbfpredict does not appear to be a Mathworks function so I do not know what parameters it takes or in what order.

[Walter Roberson]

What are you minimizing? Your Xq appears to be a vector. Are to we understand that you should have written,

x0 = rand;
[best_x, Yq] = fmincon( @(xq) rbfpredict(model, Xtr, Xq), x0, A, B, Aeq, Beq, LB, UB, [], options);

and that you are looking for the scalar Xq that gives the smallest (or most negative) prediction, yq ?

Answer 2

[Matheus]

Hello,

I am sending the function.