Using many anonymous functions seems to be an overly complex approach: why not just use numeric arrays and indexing? Then the summation would be trivial.
EDIT: in fact, the more I look at this code, the less sense it makes. For example:
1. you overwrite V_init with a function handle:
V_init = 0.5;
for i = 3:5 % compute sojourn time for row 1
...
V_init = @(x) V_fun{i};
...
end
but nowhere in your code do you call that function handle, you seem to keep treating it as an array.
2. you never define any functions in the first two cells of V_fun or EW_fun, so multiplying non-existent functions is unlikely to be very effective (btw. this is likely to be the cause of the first error). It is also a major point you would need to consider in your algorithm.
3. The function(?) f is undefined (I guess you meant h):
fun = cellfun(@(g,h) @(x) g(x).*f(x),...
4. In multiple locations you try to multiply a function handle with a numeric, e.g.: 0.9*V_fun{i}. Numerics can be multiplied with numerics, logicals, chars, but not with function handles (you need to call the function handle first).
5. Many of the anonymous functions' input arguments remain unused:
EW_fun{i} = @(x) ES(1,i)*(1+0.5*(1+SCV(1,i))*0.9*V_fun{i}*ES(1,i)/(1-0.9*V_fun{i}*ES(1,i)));
% ^ unused
V_init = @(x) V_fun{i};
% ^ unused
fun{i} = @(x) V_fun{i}*EW_fun{i};
% ^ unused
V_init = @(x) V_fun(j);
% ^ unused
V_init = @(x) V_fun{i};
% ^ unused
While this is not an error, given the nature of your calculations it should be checked.
7. Even if you manage to fix all of those (and any other) bugs, your code will be very inefficient compared to simple MATLAB code using numeric arrays, as well as being difficult to understand and maintain.
Basically you should throw this code away and start again. Do not write lots and lots of code (without testing anything) and then just expect it to run: write one line and then test it.
Do not start with the next line until that line does what you need it to do.
I very much doubt that your approach with anonymous functions is a good one. Most likely you should just write a proper function and use basic MATLAB arrays, indexing, and vectorized code.
"I need to find the minimum value of the function using fmincon or fminsearch"
For that you do not need one thousand functions, just one is required.
