"solver stopped prematurely" when using fmincon with constraints

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); % deterministic component, a mean-price level mu
    x(t) = s-f; % stochastic component
    e = x(t) - x(t-1) + p(3)*x(t-1); % error term = dx + alpha *x_t-1
    L = normpdf(e, 0, p(2));
    LL = LL + log(L);
end
f=-LL; % -sign because of minimization, and I need maximization

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:

a =  0.0079    0.3046    1.1796

However, the third element (alpha), should not exceed 1... hence my attempt to use constraints. Thanks in advance.

Answer 1

[Matt J]

Try using fmincon's sqp algorithm or the interior-point instead of the default. These will enforce lb,ub bounds rigorously (or try to) at all iterations. Accordingly, do not use general linear inequality inputs A,b to specify simple upper & lower bounds. Use the lb,ub inputs instead.

As a more minor remark, it is also not great to use global variables

 global y

Follow the guidelines here for using anonymous or nested functions to attach fixed data to a function.