Initial value problem for fmincon

Hi,

I am trying to estimate 4 parameters for the following problem:

y = p(3) + p(4)*x + e

where e follows a two parameter(p(1), p(2)) weibull distribution.

The weibull parameters have to positive and the e(errors) have to be non-zero. These constraints have been incorporated in the fmincon function.

I have calculated the maximum likelihood :

Code:

--------------------------

clc

clear all

ydata=[-0.0102535; 3.465384; 1.339983; 0.1214859; 0.7818025; 0.7275869; 0.0531813; 5.575462; 3.08733; 1.080223; 1.737704; 2.061353; 0.5685122; 0.2161634; 1.110085; -0.1119129; 2.052543; 6.476873; 16.63553; 2.541557];  

xdata=[0.2088342; 0.2623518; 0.2588278; 0.1772731; 0.1788281; 0.2012366; 0.1700758; 0.2797128; 0.2659542; 0.1669172; 0.4481468; 0.3407996; 0.2022935; 0.1687582; 0.2514656; 0.1750669; 0.2683606; 0.5407576; 0.9437701; 0.2935103];

p_initial = [2; 2; 0.1; -1.3];

A = zeros(20,1);

B = ones(20,1);

options=optimset('Display','iter','Algorithm', 'interior-point','MaxIter',10000,'TolX',10^-30,'TolFun',10^-30,'MaxFunEvals',400);

[p,fval] = fmincon(@(p) tryseven((p),xdata, ydata), p_initial,[A A B xdata],[ydata],[],[],[0; 0; -Inf; -Inf],[],[],options)

where @tryseven fucntion is the likelihood function:

   function logl = tryseven(p, xdata, ydata)

a = p(1);

b = p(2);

f = p(3);

g = p(4);

h = size(xdata,2)*log(a);

i = size(xdata,2)*log(b);

j = (b-1)*(log(ydata - f - g*xdata));

k = a*((ydata - f - g*xdata).^b);

logl = [-sum(j(:)) + sum(k(:) -h -i)];

end

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The problem is that my solution critically depends on the initial values that I choose. Can you tell me how to choose these initial values optimally?

Thanks alot!

Regards,

Prachi

[Prachi Singh]

A related answer : http://in.mathworks.com/matlabcentral/answers/274532#answer_214430