How to use a Loop in an optimization problem?

Ana Rita Rodrigues

2016 11 24

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Hi everyone, I'm trying to find out an optimal capital structure, which means to find out the optimal variable c that maximizes -g(c). In order to do that I need first to solve a nonlinear system, which is my function Fun(x), for a given initial c0 and x0. Then using the optimal value x, I can find the value c that maximizes the -g(c). My problem is that I want to make a loop that stops when the value of c using in the nonlinear system is the same that the obtained value from the maximization problem, but everything I try it's not working.

My main code is:

    function [x,c,err]=newdim3(Fun,x0,c0,~)
    global xi tau_e tau_i r mu k epsilon; 
    tol=10^(-3);
    c=c0;
    x=x0;
        for j=1
           options=optimset('MaxFunEvals',1E5,'MaxIter',1E5,...
          'TolFun',1E-32,'TolX',1E-32,'TolCon',1E-32);
           [y,fval]=fmincon(@(y) Fun(y),x,[],[],[],[],...
    [0 1 -Inf -Inf -Inf -Inf],[1 Inf Inf Inf Inf Inf],[],options);
           a1=y(3);a2=y(4);b1=y(5);b2=y(6);
           if (c>1)
                tau_e3=tau_e*epsilon;
           else
                tau_e3=tau_e;
           end  
           options=optimset('Display','iter','TolFun',1e-8);
           g = @(C,y) -xi*((1-tau_e3)*((1/(r-mu))-(C/r))+...
         a1+a2+(1-k)*(((1-tau_i)*C/r)+b1+b2));  
           C = fminbnd(@(C) g(C,x),0,y(2),options);
           err=abs(C-c);
           relerr=err/(abs(C)+tol);
           if (err<tol|relerr<tol)
               c=C;
               break;
           end 
           c=C;
           x=y;
           iter=j;
        end
    return