I'm trying to optimize the expectation of a log of a sum of random variables. Say, x(:,1:n) = observations of n differently distributed, correlated random variables.
for i = 1:n
temp = temp + c(i+1).*x(:,i);
end
temp = c(1).*temp;
pd = fitdist(temp,'Kernel');
fun = @(x) log(1+x).*pdf(pd,x);
a = integral(fun,-100,10000);
I'm using fmincon to maximize a by finding the optimal vector c. The nonlcon function that I'm using makes sure that:
t = fminsearch(@(x)(cdf(pd,x)-0.05).^2,0);
c = alpha - t;
ceq = 0;
Thus, alpha - t <= 0.
All c elements are constrained to be between 0 and 1 and c(2:n+1) have to sum to 1.
When I use fminsearch with these functions, c(1) is correct, but c(2:n+1) are all roughly the same and that's wrong. Without the nonlinear constraint the script works well and if I replace the integral with a sum over the data points, it works fine with nonlcon as well.
It seems that optimization of an integral is incompatible with nonlinear constraints... What could the problem be? How could I avoid it?
