fmincon very slow for a small scale problem

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]

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]

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.

Answer 1

[Matt J]

Don't use Symbolic Toolbox operations. Remove all the sym operations and just convert fnsum to a numerical objective function.

[Walter Roberson]

objd = matlabFunction(PV,'Vars',{[Y(:)]}); 

is converting it to a numeric objective function.

[Hassan Benchekroun]

When I tried this I get this error

Error using sym/subs>normalize (line 231)
Entries in second argument must be scalar.

Error in sym/subs>mupadsubs (line 157)
[X2,Y2,symX,symY] = normalize(X,Y); %#ok

Error in sym/subs (line 145)
    G = mupadsubs(F,X,Y);

Error in subs (line 68)
    r_unique_name = subs(sym(f_unique_name),varargin{:});

Error in S29c_essai>@(YY)double(subs(PV,Y,YY)) (line 20)
obj0 = @(YY) double(subs(PV,Y,YY));

Error in S29c_essai (line 21)
obj0(YY0)

The new code used is here

tic
clear all

T=4;
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=zeros(1,t+1);
netrev=zeros(1,t);
Y=[ones(1,t).*0.05];

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

[Matt J]

clear all
T=20;
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);

lb=ones(T,1)./1000;
A=[];b=[];
Aeq=[];beq=[];


RhoPowers=rho.^(0:T-1);

objd=@(Y) fnsum(Y,RhoPowers,X0,r,delta,rho,beta,K);

tic
[Yopt,fval]=fmincon(objd,Y0,A,b,[],[],lb,[]);
toc %Elapsed time is 0.828706 seconds.


function summt= fnsum(Y,RhoPowers,X0,r,delta,rho,beta,K)

   t=length(RhoPowers);

    X=zeros(1,t+1);
    X(1)=X0;
    netrev=zeros(t,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

    summt=RhoPowers*netrev - ((rho).^(t)).*((log(r*X(t+1).*(1-X(t+1)./K))+beta*log(X(t+1)))./delta);
    
end

[Hassan Benchekroun]

Fantastic! That's great.

Thanks a lot

Hassan

[Matt J]

objd = matlabFunction(PV,'Vars',{[Y(:)]}); is converting it to a numeric objective function.

Very sub-optimally, it would seem.

[Hassan Benchekroun]

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.