'fmincon' and how to declare parameters without 'global'

Hi All,

I am trying not to use "global" to declare shared parameters as someone suggested that it causes problems. But I have not been able to include the parameters in the function properly. I am using "fmincon". I've posted the error and warning message I am getting below the code. The code is simple, it just has too many constants and the model is multiplicative, makes it look complex. I was wondering if I am correctly declaring the parameters by including them in the function.

close all
clear all
clc
T=100;
a=0.6;        
a1=0.16;
a2=0.24;
tauw=0.5;  
tauc=1;     
Thetac=0.02;    
Thetaw=0.02;
gammac=0.02;  
gammaw=0.01;  
lambda=0.1;

sigma=3;       
phic=50;        
phiw=110;        

nu=1;      
eta=0.6;       

%Initial values

Ac0=10;          
Aw0=89;
Nc0=1;
Nw0=1;

Sw0=570
Sc0=430

Ec=zeros(T,1);Ew=zeros(T,1);
Yc=zeros(T,1); Yw=zeros(T,1);
Y=zeros(T,1);
xc=zeros(T,1);xw=zeros(T,1); 
Ac=zeros(T+1,1); Aw=zeros(T+1,1);
Ac(1,1)=Ac0;Aw(1,1)=Aw0;
Pc=zeros(T,1); Pw=zeros(T,1);
pc=zeros(T,1); pw=zeros(T,1);
cc=zeros(T,1); cw=zeros(T,1);
Nc=zeros(T+1,1);Nw=zeros(T+1,1); 
Nc(1,1)=Nc0; Nw(1,1)=Nw0;
Sc=zeros(T+1,1); Sw=zeros(T+1,1);
Sc(1,1)=Sc0;  Sw(1,1)=Sw0;   
Lw=zeros(T,1);Lc=zeros(T,1);
Xw=zeros(T,1);Xc=zeros(T,1);
Pic=zeros(T,1);Piw=zeros(T,1);

for t=1:T
A=[Ac(t),Aw(t)];
Xc(t)=Sc(t)/(Ac(t)^lambda);
cc(t)=phic*(1+1/(Sc(t)+Xc(t))^gammac);
cw(t)=phiw*(1+1/(Sw(t)+Xw(t))^gammaw);
c=[cc(t),cw(t)];
      x0=[Nc(t),Nw(t)];
      UB=[10^12*ones(T,1); 10^12*ones(T,1)]; % upper bound for the optimization
      LB=[zeros(T,1); zeros(T,1)]; % lower boud for the optimization
      options=optimset('Algorithm','active-set','TolFun',1e-11,'TolX',1e-9);
      out1=fmincon(@productivity_vL1,x0,[],[],[(1+tauw)*Aw(t),-(1+tauc)*Ac(t)],0,LB,UB,[],A,eta,nu, a,c, a1, a2, sigma,tauc,tauw,Thetac,Thetaw,options); 

      Nc(t+1)=out1(1);
      Nw(t+1)=out1(2);
      Ac(t+1)=(1+tauc*Thetac)*Ac(t);
      Aw(t+1)=(1+tauw*Thetaw)*Aw(t);
  Pc(t)=((Aw(t)/Ac(t))^(1-a1)*(cc(t)/cw(t))^a2)/(1+((Aw(t)/Ac(t))^(1-a1)*(cc(t)/cw(t))^a2)^(1-sigma))^(1/(1-sigma));
  Pw(t)=(1-Pc(t)^(1-sigma))^(1/(1-sigma));
  Lc(t,1)=Pc(t)^(1-sigma);
  Lw(t,1)=1-Lc(t);

Ec(t)=(a2/cc(t)*Pc(t)^(1/(1-a1))*Lc(t)^((1-a)/(1-a1))*Ac(t+1))^((1-a1)/(1-a1*(1+a2))*(1-a2));
Ew(t)=(a2/cw(t)*Pw(t)^(1/(1-a1))*Lw(t)^((1-a)/(1-a1))*Aw(t+1))^((1-a1)/(1-a1*(1+a2))*(1-a2));

Sc(t+1)=Sc(t)+Xc(t)-Ec(t)/Ac(t)^lambda;
Sw(t+1)=Sw(t)+Xw(t)-Ew(t);

FUNCTION

    function F=productivity_vL1(x,A,eta,nu, a, a1, a2, c, sigma,tauc,tauw,Thetac,Thetaw)

    Nc=x(1);
    Nw=x(2);

    Thetac=nu*(Nc/((1+tauc)*A(1)))^eta;
    Thetaw=nu*(Nw/((1+tauw)*A(2)))^eta;
    Ac1=(1+tauc*Thetac)*A(1);
    Aw1=(1+tauw*Thetaw)*A(2);

    p1=1+1/((1-a)*(1-sigma))+(a2*(1+(1-a)*(1-sigma)))/((1-a)*(1-sigma)*(1-a1*(1+a2)));

    Lc=((Nc^(1-eta)/(nu*eta*a1*(1-a1)))^((1-a1)/(1-a))*(a2/c(1)*Ac1)^(-a2*(1-a1)/((1-a)*(1-a1*(1+a2)))))^(1/p1);
    Lw=((Nw^(1-eta)/(nu*eta*a1*(1-a1)))^((1-a1)/(1-a))*(a2/c(2)*Aw1)^(-a2*(1-a1)/((1-a)*(1-a1*(1+a2)))))^(1/p1);

    F=Lc+Lw-1;

The error message I am getting is below

Warning: Struct field assignment overwrites a value with class "double". See MATLAB R14SP2 Release Notes, Assigning Nonstructure Variables As Structures
Displays Warning, for details. 
> In createOptionFeedback at 33
  In prepareOptionsForSolver at 31
  In fmincon at 210
  In paper2_vL1 at 85 
Warning: Length of lower bounds is > length(x); ignoring extra bounds. 
> In checkbounds at 27
  In fmincon at 317
  In paper2_vL1 at 85 
Warning: Length of upper bounds is > length(x); ignoring extra bounds. 
> In checkbounds at 41
  In fmincon at 317
  In paper2_vL1 at 85 
Warning: Struct field assignment overwrites a value with class "double". See MATLAB R14SP2 Release Notes, Assigning Nonstructure Variables As
Structures Displays Warning, for details. 
> In fmincon at 363
  In paper2_vL1 at 85 
Attempted to access A(2); index out of bounds because numel(A)=1.

Error in productivity_vL1 (line 11)
Thetaw=nu*(Nw/((1+tauw)*A(2)))^eta;

Error in fmincon (line 564)
      initVals.f = feval(funfcn{3},X,varargin{:});

Error in paper2_vL1 (line 85)
    out1=fmincon(@productivity_vL1,x0,[],[],[(1+tauw)*Aw(t),-(1+tauc)*Ac(t)],0,LB,UB,[],A,eta,nu, a,c, a1, a2, sigma,tauc,tauw,Thetac,Thetaw,options);

Caused by:
    Failure in initial user-supplied objective function evaluation. FMINCON cannot continue.

Answer 1

[dpb]

Per the doc's, the function for fmincon is a function that accepts a vector x and returns a scalar f. You've got a whole lot of other stuff in there as well; that doesn't meet the specification and so fmincon is thereafter all confused...

function F=productivity_vL1(x)

is all you can have as the function that is the one whose handle is passed to fmincon

As referenced in the links in the doc, you have the choices of either using an anonymous function which includes the other constants within it explicitly, a secondary file that uses a nested function and which calls fmincon from the visible function which accepts all the other variables or the global solution.

I don't have the time at the present to try to decipher just who's who in the zoo in your function to try to recast it, but the link to current doc for the issue is at

http://www.mathworks.com/help/optim/ug/passing-extra-parameters.html

along with links to some more complex cases as guides.

It is unfortunate that TMW didn't include a user-definable array or structure arrangement in the user interface to make this an easier process than it is, but they chose not to so we have this to deal with...

Answer 2

[mrrox]

Thank you very much guys!