A question about fmincon

I have a object function(f(x)), which is nonlinear,with 3 parameters(say a,b,c). I want to find the max value of this function by changing these parameters subject to some constraints(st1: a>0,b>0,c>0.st2:b+c<1). Because I want to the max value not the min value, I change the object function to -f(x) so that fmincon could give me the max value of f(x). However when I type

A = [0,1,1];

b = 1;

initial = [0.00002,0.03,0.9] ;

lb = [0,0,0];

[x,fval] = -fmincon(@SimpleGARCH_1_1,initial,A,b,[],[],lb,[]) fmincon gives me this answer:

Warning: The default trust-region-reflective algorithm does not solve problems with the constraints you have specified. FMINCON will use the active-set algorithm instead. For information on applicable algorithms, see Choosing the Algorithm in the documentation. > In fmincon at 486

Solver stopped prematurely.

fmincon stopped because it exceeded the function evaluation limit, options.MaxFunEvals = 300 (the default value).

x =

      NaN +    NaNi      NaN +    NaNi      NaN +    NaNi

fval =

      NaN +    NaNi

I don't know what happened...I'm just a beginner of Matlab. The following is my code. I want to know what should I do to get the right answer. I use the same data with Excel Solver and I can get the right answer.

function [Sum_MLE] = SimpleGARCH_1_1(initial)

%SIMPLEGARCH_1_1 Summary of this function goes here

% Detailed explanation goes here

% This function calcualate the updataed volatility using a GARCH(1,1)

% process % % Inputs:

% 1- initial: a 3*1 vector which contains the initial value for % omega,alpha and beta.

% % omega = 1.67073058944028E-06;

% alpha = 0.0625323009098825;

% beta = 0.900001208378727;

load JPY

price = JPY;

Return = diff(price)./price(1:end-1);

% arithmetic return, we could also use log return

Returnsquare = Return.^2;

NumReturn = length(Return);

omega = initial(1);

alpha = initial(2);

beta = initial(3);

Vol = zeros(NumReturn-1,1);

Likelihood = zeros(NumReturn-1,1);

Vol(1) = Returnsquare(1);

for i = 2:NumReturn-1

   Vol(i) = omega+alpha*Returnsquare(i)+beta*Vol(i-1);

end

% Likelihood(1:end) = -log(Vol(1:end))-Returnsquare(2:end)./Vol(1:end);

Likelihood(1:end) = log(Vol(1:end))+Returnsquare(2:end)./Vol(1:end);

%this is because there is no max function in matlab, so we use -Likelihood and find its min value so that we find the max value of Likelihood

Sum_MLE = sum(Likelihood);

end

[Andrew Newell]

I'm having trouble reproducing your problem. I don't have the file JPY, so I put in a random vector, and got an answer. I see one error:

[x,fval] = -fmincon(@SimpleGARCH_1_1,initial,A,b,[],[],lb,[]);

is an invalid use of UMINUS because there are two outputs. Use this instead:

[x,fval] = fmincon(@SimpleGARCH_1_1,initial,A,b,[],[],lb,[]);

x = -x; fval = -fval;

If JPY is small, it would help if you provided the contents.