I am trying to solve a non linear optimization with constraints. It is a simple mean-reversion model, with log-likelihood maximization. It looks likes this: Vector p contains three parameters to be optimized. p(1) = mu, a constant. p(2) = sigma, the standard deviation (so larger than 0). p(3) = alpha, representing mean-reverting behaviour (so between 0 and 1).
p0 = [10 1 0.9];
A = [0 0 1;
0 0 -1
0 -1 0];
b = [ 1;0; 0];
[a fval] = fmincon( @LogLikMeanRev,p0, A,b)
My function LogLikMeanRev is as follows:
function [ f ] = LogLikMeanRev( p )
global y
T = length(y);
x = zeros(T, 1);
LL = 0 ;
for t = 2:T
s = y(t);
f = p(1);
x(t) = s-f;
e = x(t) - x(t-1) + p(3)*x(t-1);
L = normpdf(e, 0, p(2));
LL = LL + log(L);
end
f=-LL;
end
This code is after a handbook. The output I get are all "NaN" and the warning is "Solver stopped prematurely. fmincon stopped because it exceeded the function evaluation limit, options.MaxFunEvals = 300 (the default value)."
When I leave the constraints out (that is, optimize with fminsearch), I get a nice response:
However, the third element (alpha), should not exceed 1... hence my attempt to use constraints. Thanks in advance.
