Simple minimization algorithm in a while loop?

Hello,

I have a program (call it blackbox) and I give this program a value (zo) and it does a calculation and checks if the result (diff) is within a certain tolerance (tol).

What I would like to do is to have it minimize in as few iterations as possible. It would be ideal to have the steps increase/decrease dynamically. Anyone have suggestions?

Here is what I was thinking.

%input value to start
zo = 15;

% +/- tolerance
tol = 0.1;

% start while loop
diff = 1;
count = 0;

while abs(diff) > tol
    % black box algorithm
    diff = zo/2 - 2
    % check if value is within the tolerance

      % is there a better way to do this in less iterations?
      if diff > tol
          zo = zo - 0.1; 
      elseif diff < -tol
          zo = zo + 0.1;
      end

      count = count +1
  end

[Norris]

Edit: I realized the code was very poorly written and didnt really get at what I wanted to do. I hope its easier to understand now.

I want to be able to minimize the error with the least amount of iterations possible.

[Adam]

I assume those hard-coded 0.1 values should be ' tol ' instead? Or do you really want to always add/subtract -0.1 irrespective of if you change the value of tol ?

Answer 1

[Adam]

      zo = 5;

      tol = 0.1;

      diff = 100; % Doesn't matter so long as it is outside of tolerance

      count = 0;

      while abs( diff ) > tol
         diff = blackbox( z0 );

         z0 = z0 - sign( diff-tol ) * tol;
         count = count + 1;
      end

looks like it does what you want unless I am missing something. That is only based on a quick assessment of your code.

Obviously you can add in printing stuff out to command line if you wish.

[Norris]

Thanks but I was wanting to have zo update to a new value so that 'diff' is minimized to within the tolerance.

Edit: I cleaned up the code a bit and added some lines to show where I need the algorithm

[Adam]

It's impossible really to advise on how best to minimise a blackbox function. I have no idea whether the function is well behaved or not. Changing z0 by even 0.1 could have a huge impact on results depending on the function.

Good optimisation algorithms are usually tailored towards the problem with some kind of knowledge of the domain.

e.g. if the output from your blackbox function is a nice parabola based on the input then it is trivial to minimise to within a tolerance. If the output of function is, to all intents and purposes, arbitrary relative to the input then that obviously isn't the case.

[Norris]

Sorry for the late reply.

Thanks for your suggestion. My blackbox function is a flow model which requires a number of input parameters.