script for a Function

Hello,

I have a function

 y = 5 + 2*a - 3*b + 8*c + a*b

where a,b,c are variables such that: the values of

              a = 4,6,8      
              b = 12,16,18
              c = 1,3,9

How to write a script defining this function to used by an optimizing algorithm

[Walter Roberson]

Is the question which combination of values of the variables gives the lowest result?

Answer 1

[Walter Roberson]

Vectorize the expression of the equation.

Create grids of the permitted values using ndgrid or meshgrid .

Use the grid of values in the expression.

min() or max() to find the optimal result.

[Ahmed Elsadek]

Thank you for feedback I just want to define the function to be used by another code. I want Matlab to know that I have a function of one dependent variable (y) and three independent ones (a,b,c) and each of a,b and c have certain values only (the ones that I mentioned in my original question) this script will be saved to be used by another code.

[Walter Roberson]

Supposing that y is a function handle that is not necessarily vectorized:

function [fval, best_a, best_b, best_c] = discrete_nonlin_optimize(y, a, b, c)
 [A, B, C] = ndgrid(a, b, c);
 values = arrayfun(y, A, B, C);
 [fval, idx] = min(values);
 best_a = A(idx);
 best_b = B(idx);
 best_c = C(idx);

In the special case that y is known to be vectorized,

function [fval, best_a, best_b, best_c] = discrete_optimize(y, a, b, c)
 [A, B, C] = ndgrid(a, b, c);
 values = y(A, B, C);
 [fval, idx] = min(values);
 best_a = A(idx);
 best_b = B(idx);
 best_c = C(idx);

This would be more efficient than the arrayfun version.

If your a, b, and c are quite large, you could run out of memory forming A, B, C. In that case you would have to change strategies, such as using ga() with integer constraints.