MATLAB optimization of the function - matlab

Question

I want to optimize this function:
function Y_res = GetY( Y, P )
cnt = length(P);
denom = 0;
for i = 1:cnt
Y(i) = rand;
denom = denom + P(i) / (1 - Y(i));
end
Y_res = 1 - 1 / denom;
Y
Y_res
end
This function receives Y and P. P is a constant array. I need to optimize Y array values. And I trying to do this:
Y = [0.3 0.2 0.1]; % need to be optimized
P = [0.65 0.2 0.15]; % constant array
fhnd_GetY = #(x) GetY(Y, P);
options = optimset('TolX', 1e-3);
optimal_x = fminbnd(fhnd_GetY, 0.2, 0.4, options);
But the result of optimal_x variable does not equals to Y_res, which you can see on the screen during iterations of GetY function. Why? I need to optimze Y_res between 0.2 and 0.4 for example. So as a result I need to receive Y_res between 0.2 and 0.4 (for example) and Y array with values by means of which I can receive Y_res.

Answer 1

Assuming that you only intend to optimize the function GetY and given the fact that you are creating Y inside it and as such don't need to externally input Y into it, see if this modified function is optimized enough for you -
function [Y_res,Y] = GetY( P )
found = false;
while ~found
Y = rand(size(P));
Y_res = 1-1./sum(P./(1-Y));
if Y_res>0.2 & Y_res<0.4
found = true;
end
end
return;
Please note that if you don't need Y as an output, you can use Yres = GetY([0.65 0.2 0.15]) instead, but most probably you would need that (my guess though).
Few sample runs -
>> [Yres,Y] = GetY([0.65 0.2 0.15])
Yres =
0.3711
Y =
0.4243 0.2703 0.1971
>> [Yres,Y] = GetY([0.65 0.2 0.15])
Yres =
0.2723
Y =
0.1897 0.4950 0.1476
>> [Yres,Y] = GetY([0.65 0.2 0.15])
Yres =
0.3437
Y =
0.3624 0.0495 0.4896