fminsearch taking too much time - results do not show up yet

 % 
function A=obj(b,Y, YL, tempcyc, cyc, Yzero, age, agesq, educ, ageav, agesqav, educav, qv, year1, year2, year3, year4, year5, year6, year7, workregion1, workregion2, workregion3, workregion4, workregion5, workregion6, workregion7, workregion8, workregion9, workregion10, workregion11, workregion12, workregion13, workregion14, workregion15, workregion16, qw)
%
A=0;
for i=1:715
S=0;
for m=1:12
P=1;
for t=1:8
P=P*(normcdf((2*Y(i,t)-1)*(b(1)*YL(i,t)+b(2)*tempcyc(i,t)+b(3)*cyc(i,t)+b(4)*Yzero(i,t)+b(5)*age(i,t)+b(6)*agesq(i,t)+b(7)*educ(i,t)+b(8)*ageav(i,t)+b(9)*agesqav(i,t)+b(10)*educav(i,t)+b(11)*1+b(12)*sqrt(2)*qv(m,1)+b(13)*year1(i,t)+b(14)*year2(i,t)+b(15)*year3(i,t)+b(16)*year4(i,t)+b(17)*year5(i,t)+b(18)*year6(i,t)+b(19)*year7(i,t)+b(20)*workregion1(i,t)+b(21)*workregion2(i,t)+b(22)*workregion3(i,t)+b(23)*workregion4(i,t)+b(24)*workregion5(i,t)+b(25)*workregion6(i,t)+b(26)*workregion7(i,t)+b(27)*workregion8(i,t)+b(28)*workregion9(i,t)+b(29)*workregion10(i,t)+b(30)*workregion11(i,t)+b(31)*workregion12(i,t)+b(32)*workregion13(i,t)+b(33)*workregion14(i,t)+b(34)*workregion15(i,t)+b(35)*workregion16(i,t))));
end
%
S=S+qw(m,1)*P;
end
%
A=A+log(S/sqrt(pi));
A=-A;
end

This is my objective function I am minimizing (actually maximizing; I am minimizing -A) and the parameters I am estimating is b=[b(1)............b(35)]. Y, YL, tempcyc,.........., qw are matrices that I am imported as data. The objective function consists of a product(across t=1:8T) nested within a sum (across m=1:12) that is in turn nested within a sum (across n=1:715). And below is my code using fminsearch for my unconstrained minimization.

    % %%Minimization
start=[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0];
iter=50000;
options=optimset('Display','iter','MaxIter',iter,'MaxFunEvals',100000); 
[b, fval, exitflag, output]=fminsearch(@(b)obj(b,Y, YL, tempcyc, cyc, Yzero, age, agesq, educ, ageav, agesqav, educav, qv, year1, year2, year3, year4, year5, year6, year7, workregion1, workregion2, workregion3, workregion4, workregion5, workregion6, workregion7, workregion8, workregion9, workregion10, workregion11, workregion12, workregion13, workregion14, workregion15, workregion16, qw), start, options);%
%%Results
fprintf('[b] : % 1.4e % 1.4e %1.4e % 1.4e % 1.4e % 1.4e \n',...
   b(1),b(2),b(3),b(4), b(5),b(6),b(7),b(8), b(9),b(10),b(11),b(12), b(13),b(14),b(15),b(16), b(17),b(18),b(19),b(20), b(21),b(22),b(23),b(24), b(25),b(26),b(27),b(28), b(29),b(30),b(31),b(32), b(33),b(34), b(35));
  end

The problem is that the optmization results do not show up even after 12+ hours (It is still reflecting, expanding, contracting inside, etc.) Could someone give me an idea on how to make the process faster?

Thank you.

Answer 1

[Matt J]

35 unknown variables is way too big for fminsearch. It's theoretically guaranteed to converge for only 1 unknown, and gives good empirical results for up to about 6.

You will probably need an Optimization Toolbox solver.

[Matt J]

The objective function consists of a product(across t=1:8T) nested within a sum (across m=1:12) that is in turn nested within a sum (across n=1:715). And below is my code using fminsearch for my unconstrained minimization.

Such operations are easily vectorized using MATLAB commands. You should consider doing so to improve speed-efficiency of your code. It looks like the whole thing boils down to something of the form

    G=reshape(  prod(normcdf(M*b) ,2)  , 12,715);
    S=sum(qw.'*G);

for an appropriate matrix M.