[HELP!!!!] Run fmincon repeatedly

Hi all

I am trying to minimize the objective function over (x(1),x(2)):

           exp(x(1))*(4*x(1)^2+2*x(2)^2+4*x(1)*x(2)+2*x(2)+1)+b

subject to constraint

              (x(1))^2+x(2)-1+b=0,       (notice that b is also in constraint)
              -x(1)*x(2)-10<=0.

I want to run the optimization 20 times , for b=1, b=2, b=3.....b=20 ( because b is between 0 to 20). I also want to store the optimal (x(1),x(2),b) so that I can plot it later.

There are existing reference ((<http://www.mathworks.com/help/optim/ug/nonlinear-equality-and-inequality-constraints.html)>) which I followed. How do I modify the following code so that it will do the above?

Step 1: Write a file objfun.m.

function f = objfun(x)
f = exp(x(1))*(4*x(1)^2+2*x(2)^2+4*x(1)*x(2)+2*x(2)+1)+b;

Step 2: Write a file confuneq.m for the nonlinear constraints.

function [c, ceq] = confuneq(x)
% Nonlinear inequality constraints
c = -x(1)*x(2) - 10;
% Nonlinear equality constraints
ceq = x(1)^2 + x(2) - 1+b;

Step 3: Invoke constrained optimization routine.

x0 = [-1,1];            % Make a starting guess at the solution
options = optimoptions(@fmincon,'Algorithm','sqp');
[x,fval] = fmincon(@objfun,x0,[],[],[],[],[],[],... 
   @confuneq,options);

Answer 1

[Alan Weiss]

You might want to consult the documentation on passing extra parameters. Either anonymous functions or nested functions will work for your case.

Alan Weiss

MATLAB mathematical toolbox documentation