fmincon and patternsearch initial point
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I had initially planned to use fmincon as my optimization method, but as I varied initial points, I was receiving enough variation in output that I thought perhaps there were several local minima. While this didn't entirely make sense, I tried using patternsearch to find a global solution.
clc
clear
%options=optimoptions('fmincon', 'Display', 'iter', 'OptimalityTolerance', 10.0000e-06, 'StepTolerance', 10.0000e-10)
Lmax=.25;
r=.03;
Xfix=.5;
p=.35;
w=40000;
year=80;
growa=12.91;
growb=223.71;
C=20000;
A=[-1 0;0 -1];
b=[0;0];
Aeq=[-1 0];
beq=[-.25];
z=[];
h=[];
iteration=[];
%for m=1:5;
x0=[.1 40];
for n=1:9
utility=@(x)-1*((Lmax-x(1)/(1-exp(-r*x(2))))^(.1*n)*((w*year*Xfix)/r+x(1)*((exp(-r*x(2))*p*exp(growa-growb/x(2))-C)/(1-exp(-r*x(2)))))^(1-.1*n));
[y,fval]=fmincon(utility,x0,A,b,Aeq,beq);
%[y,fval]=patternsearch(utility,x0,A,b,Aeq,beq);
z=[z;y];
h=[h;fval];
iteration=[iteration;n];
end
g=[iteration z h];
min(fval);
i=[z(:,1)];
j=[z(:,2)];
%plot3(i,j,h)
%end
format long g;
g
pattersearch appears to only returns an answer when initial point is [0 0]. And by my math, it doesn't seem to be returning a minimum. There is definitely something I'm missing.
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