Problem with fmincon and many starting values

1 Ansicht (letzte 30 Tage)
MRC
MRC am 13 Feb. 2014
Bearbeitet: Matt J am 13 Feb. 2014
Hi all, I'm trying to code the following minimization problem using fmincon and many starting values but I get error messages because the objective function has the log function inside. How can I solve this problem? Here the code. Thank you!
n=2;
thetatrue=[1 1 2 2 0.2];
mu = [0 0];
sd = [1 thetatrue(2*n+1); thetatrue(2*n+1) 1];
load data
X=data(:,1:n);
Y=data(:,n+1:size(data,2));
A1(:,2)=-X(:,1);
A1(:,1)=-1;
A2(:,2)=-X(:,2);
A2(:,1)=-1;
W1=(all(bsxfun(@eq,Y,[0 0]),2));
W2=1-W1;
cdfun=@(x) mvncdf( [A1*[x(1);x(3)], A2*[x(2);x(4)] ]...
,mu,[1 x(5); x(5) 1]);
options=optimset('Algorithm','interior-...
point','Display','iter','MaxIter',10000,'TolX',10^-30,'TolFun',10^-30);
% Grid of starting values for fmincon
alpha1=normrnd(thetatrue(1),1,1,5); %random draws from N(alpha1true,1)
alpha2=normrnd(thetatrue(2),1,1,5); %random draws from N(alpha2true,1)
beta1=normrnd(thetatrue(3),1,1,5); %random draws from N(beta1true,1)
beta2=normrnd(thetatrue(4),1,1,5); %random draws from N(beta2true,1)
rho=(-0.9:0.1:0.9);
CC = {alpha1,alpha2,beta1,beta2,rho};
b = cellfun(@numel,CC);
n1 = cumsum(b);
a = fullfact(b);
idx = bsxfun(@plus,a,[0, n1(1:end-1)]);
v = cat(2,CC{:});
theta0grid = v(idx); %grid of starting values
L_nstar=zeros(size(theta0grid,1),1);
Exitflag=zeros(size(theta0grid,1),1);
for j=1:size(theta0grid,1) %for each starting value
theta0=theta0grid(j,:);
[theta,fval,exitflag,output]=...
fmincon(@(x) log_lik(x,cdfun,W1,W2),theta0,[],[],[],[],[-Inf; -Inf; Inf; -Inf;-0.999],[+Inf; +Inf; +Inf; +Inf; 0.999],[],options);
L_nstar(j)=-fval;
Exitflag(j)=exitflag;
end
L_nstar=max(L_nstar);
and
function val=log_lik(theta,cdfun,W1,W2)
z=cdfun(theta);
val=-sum(W1.*log(z)+W2.*log(1-z));
  1 Kommentar
MRC
MRC am 13 Feb. 2014
Bearbeitet: MRC am 13 Feb. 2014
for example when j=1, I get the following error
Error using barrier (line 22) Objective function is undefined at initial point. Fmincon cannot continue.
Error in fmincon (line 905) [X,FVAL,EXITFLAG,OUTPUT,LAMBDA,GRAD,HESSIAN] = barrier(funfcn,X,A,B,Aeq,Beq,l,u,confcn,options.HessFcn, ...

Melden Sie sich an, um zu kommentieren.

Akzeptierte Antwort

Matt J
Matt J am 13 Feb. 2014
Bearbeitet: Matt J am 13 Feb. 2014
The sqp algorithm can recover from NaN's and Infs returned by the objective function and constraints.
  3 Kommentare
MRC
MRC am 13 Feb. 2014
I have read that both interior-point and sqp can recover from Nan's and Inf's, so why is not the case here?
Matt J
Matt J am 13 Feb. 2014
Bearbeitet: Matt J am 13 Feb. 2014
I think you need a starting point that is feasible, so that they have a foothold in the feasible set.
You should probably take a closer look at your initial values and at the values of mu and sigma to see why you're getting z=0 or 1. Since z=cdfun(theta) is from a Gaussian CDF, z should always assume values strictly between 0 and 1 where log(z) and log(1-z) should not be producing undefined values. Maybe you have overflow, in which case you're choosing highly extreme theta values, or you have sigma=0 somewhere...

Melden Sie sich an, um zu kommentieren.

Weitere Antworten (0)

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by