Problems with fmin. Trying to minimize a function with two unknowns and a vector that changes

Hi, I'm still a bit new to Matlab, but I have a problem that i can't seem to figure out. I know that fminsearch or fminunc usually minimize functions(constant ones at least) such as x^2+y. I have the following equation:

-log((1/beta)*(1+xi*(l(i,1)-u)/beta)^(-1/(xi-1)))

What I am looking to minimize is the the sum of all the logs from i = 1 to N, where l(i,1) for all N is a known number, and beta and xi are unknowns. I can do minimization for each function, but I don't know to minimize for the sum.

I've looked around and I haven't found any solutions yet.

Answer 1

[Walter Roberson]

obj_fun = @(beta, xi, L, U) sum( -log((1/beta)*(1+xi*(L-U)/beta)^(-1/(xi-1))) );

l = ...
u = ...

guess = randn(1,2);
fminsearch( @(bx) obj_fun(bx(1), bx(2), l, u), guess )

If you have constraints you would use fmincon instead of fminsearch.

Also if there are local minima then you might need to use a global solver instead of a local solver.

[Ribal Abi Raad]

Hi, I tried your solution using the following piece of code:

obj_fun = @(beta,xi,l,u_n) sum(-log((1/beta)*(1+xi*(l-u_n)/beta)^(-1/xi-1))); l = loss_nu(i,1); u_n = 160; [phat] = fminsearch(@(bx) obj_fun(bx(1),bx(2),l,u_n),phat_guess) It worked fine, but the result I get is close to my phat_guess, and the result I should get is far off. I've tried with other variables for the phat_guess, and it always gives me the same numbers more or less.

[Walter Roberson]

I do not know what the value of i is there. You should be passing in an entire vector for your third parameter. And it is a good idea to not name a variable l (lower case L) as it is often difficult to tell the difference between that and the number 1.