Index Exceeds Array Bounds

I keep getting an "Index exceeds array bounds" message with the code below. I am running it as seen in the picture where the objective function and constraint functions have their own editor window and then the lifecycle code is pasted into the command window. Any idea what may be causing this?

function y=Lifecycle_Objfun(x,beta,T)
% variables: c(1),c(2),...,c(100), I(1),I(2),...,I(100)

y=sum((beta.^(0:(T-1))') .* ((c(1:100)^(1-gam))/(1-gam)));
y=-y;

end

function [cineq,ceq]=Lifecycle_ConFun(x,T,Q,A,a,initI,termI)
% variables: c(1),c(2),...,c(100), I(1),I(2),...,I(100)

cineq = [];
ceq = zeros(T+2,1);

c = x(1:T);
I = x((T+1):(2*T+1));

% transition law for I
for i=1:100
    ceq(i) = I(i) - ((A(i)*Q(i)^a-c(i));
end

% initial saving
ceq(T+1) = I(1) - initI;

% terminal saving
ceq(T+2) = I(100) - termI;

end

function lifecycle()

beta=0.96;
d=0.1;
a=0.33;
phi=0.975;
gam=2;
Iss=0.3533;
Q(1)=1;
initI=0;
termI=0;
Q(T+1)=(1-d)*Q(T)+I(T);
phi*Iss=I(T);
T=(1:100);
-c(T)=0
-Q(T)=0

% variables: c(1),c(2),...,c(100), I(1),I(2),...,I(100)
x0 = ones(2*T+1,1);
lb = zeros(2*T+1,1);
lb(1:T) = 0.01;

xsol = fmincon(@(x) Lifecycle_Objfun(x,beta,T),x0,[],[],[],[],lb,[],...
    @(x) Lifecycle_ConFun(x,T,Q,A,a,initI,termI));

c = xsol(1:T);
I = xsol((T+1):(2*T+1));

times=(1:T)';
figure
plot(times,c,'k-',[times;T+1],I,'b-','LineWidth',2)
legend('consumption','savings','Location','NorthWest');
xlabel('Time')
title('Optimal Solution of Life Cycle Problem')
set(gca,'fontsize',16)
xlim([1 T+1])
ylim([0 14])

options = optimoptions('fmincon','MaxFunctionEvaluations',100000);
xsol = fmincon(@(x) Lifecycle_Objfun(x,beta,T),x0,[],[],[],[],lb,[],...
    @(x) Lifecycle_ConFun(x,T,Q,A,a,initI,termI),options);

c = xsol(1:T);
I = xsol((T+1):(2*T+1));

figure
plot(times,c,'k-',[times;T+1],I,'b-','LineWidth',2)
legend('consumption','savings','Location','NorthWest');
xlabel('Time')
title('Optimal Solution of Life Cycle Problem')
set(gca,'fontsize',16)
xlim([1 T+1])
ylim([0 14])

end

Answer 1

[Walter Roberson]

You have

phi*Iss=I(T);

-c(T)=0
-Q(T)=0

It is not valid to have any operation other than indexing calculations on the left side of the "="

If you are trying to make statements of functional relationship, expression an equation such as

phi*Iss = (something)

then you cannot do that in that form. The closest you would be able to get to that would be to use the symbolic toolbox and use

eqn = phi*Iss == something