Optimizing a function from a given set?

Is there a way to find the optimal value of a minimized function from a given set of solutions?

Here is an example of what I would like to do:

For x in {0,0.5,1}, solve: x = arg max f(x).

I think I would need a variation of "fminbnd", as this one uses a given interval of solutions, while I need a given set of solutions.

Any suggestion would be very much appreciated. Thank you

Answer 1

[Walter Roberson]

For an explicit list of arguement values, x:

[bestfval, bestidx] = max(arrayfun(@f, x))
bestx = x(bestidx);

If the function is fully vectorized then

[bestfval, bestidx] = max(f(x(:)));
bestx = x(bestidx);

[Mohamed Larabi]

Your answer replies perfectly to the problem stated. But I made a mistake while I typed it. It is:

For x in {0,0.5,1}, solve: x = arg max x*f(y). If you have any thoughts about it, please let me know.

[Walter Roberson]

If the task is to find the y that maximizes x*f(y) for each given x, then the answer is going to be the same as the y that maximizes f(y) without considering the x because multiplication by positive x is a linear operator. If some of the x could be negative and some positive then you could have a more interesting situation.

Answer 2

[Mohamed Larabi]

The task is to find the x, while f(y) is given. I am trying to simplify my problem as much as I can to be understandable by the overall Matlab community. What I actually need to do is to numerically solve HJB (Hamilton-Jacobi-Bellman) problem. It is dynamic programming. Do you have any reference or link to share about it? Thank you very much.

[Walter Roberson]

If f(y) is given, then the x that maximizes x*f(y) is:

if f(y) > 0
  bestx = max(x);
elseif f(y) < 0
  bestx = min(x);
else
  all finite non-nan entries in x give the same result
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