# fmincon very slow for a small scale problem

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Hassan Benchekroun on 22 Oct 2020
Hello, I have been trying to use fmincon for a simple problem with a small number of variables and yet it is very slow or does not even return an answer. Could you please advise on suggestions? I have even used fminsearch since my constraints are just lower bounds on the variables and it's worse. It took 429 sec to solve this with T=9; I need to go up to 20, which should still be ok but it doesn't even return an answer.
Thanks for suggestions
tic
clear all
T=9;
r=1;
K=1;
beta=4;
delta=0.02;
rho=1/(1+delta);
X0=0.1;
Y0=[ones(1,T).*0.05]';
%YY0=ones(1,T).*0.05;
%Xstar=K*(r*(1+beta)-delta)./(r*(beta+2));
%Ystar=r*Xstar*(1-Xstar./K);
[X,Y,NETR,summm,PV] = fnsum(T,X0,r,delta,rho,beta,K);
%obj0 = @(YY) double(subs(PV,Y,YY));
%obj0(YY0)
objd = matlabFunction(PV,'Vars',{[Y(:)]});
%objd([Y0])
%Resd = matlabFunction(Res,'Vars',{[Q(:)]});
%NetrevOpt = matlabFunction(NETR,'Vars',{[Q(:)]});
%summOpt = matlabFunction(NETR,'Vars',{[Q(:)]});
lb=ones(T,1)./1000;
A=[];b=[];
Aeq=[];beq=[];
%[Yopt0,fval0]=fminsearchbnd(obj0,YY0,lb,[])
%[Yopt,fval]=fminsearch(obj0,YY0);
[Yopt,fval]=fmincon(objd,Y0,A,b,[],[],lb,[])
%[Yopt,fval]=fmincon(obj0,YY0,A,b,[],[],lb,[])
%[NetrevOpt(Qopt)]';
%[Resd(Qopt)]';
%plot(Resd(Qopt))
toc
function [X,Y,netrev,summm,summt] = fnsum(t,X0,r,delta,rho,beta,K)
X = sym('X',1:t+1);
netrev = sym('netrev',1:t);
Y = sym('Y',[1 t]);
X(1)=X0;
%a(2:end)=b(2:end)+a(1:end-1).*c(2:end);
%X(2:end)=X(1:end-1)-Y(1:end)+r*X(1:end-1).*(1-X(1:end-1)./K);
%XX=X(1:end-1);
%netrev = log(Y)+beta*log(X(1:end-1));
for i=1:t
netrev(i)= -(log(Y(i))+beta*log(X(i)));
X(i+1)=X(i)-Y(i)+r*X(i).*(1-X(i)./K);
end
n=1:t;
summm = sum(((rho).^(n-1)).*(netrev(n)));
summt=summm- ((rho).^(t)).*((log(r*X(t+1).*(1-X(t+1)./K))+beta*log(X(t+1)))./delta);
end

Walter Roberson on 22 Oct 2020
X = sym('X',1:t+1);
netrev = sym('netrev',1:t);
That declares X to be a 1 x 2 x 3 x 4 x 5 x ... t+1 object, and declares netrev to be a 1 x 2 x 3 x 4 x 5 x ... t object.
You want [1, t+1] and [1, t] instead.
Hassan Benchekroun on 23 Oct 2020
Thanks, when I tried it I got this error:
Error: File: S29b_essai2.m Line: 47 Column: 20
Invalid expression. When calling a function or indexing a variable, use parentheses.
Otherwise, check for mismatched delimiters.

Matt J on 22 Oct 2020
Edited: Matt J on 22 Oct 2020
Don't use Symbolic Toolbox operations. Remove all the sym operations and just convert fnsum to a numerical objective function.

Hassan Benchekroun on 23 Oct 2020
Fantastic! That's great.
Thanks a lot
Hassan
Matt J on 23 Oct 2020
objd = matlabFunction(PV,'Vars',{[Y(:)]}); is converting it to a numeric objective function.
Very sub-optimally, it would seem.
Hassan Benchekroun on 23 Oct 2020
Indeed, I also tried something like
obj0 = @(YY) double(subs(PV,Y,YY));
obj0(YY0)
instead of matlabFunction but also did not work.
Anyway thanks again.