MATLAB: Fmincon, find integer values as optimal values

fminconintegerpositive

 f =@(fr)(50*fr(1)^2 + 100)/fr(1) + (175*fr(2)^2 + 150)/fr(2) + (160*fr(3)^2 + 250)/fr(3)
lb = [0,0,0];
ub = [5,5,5];
A = [];
b = [];
Aeq = [];
beq = [];
fr0 = [1,1,1];
fr = fmincon(f,fr0,A,b,Aeq,beq,lb,ub)
output:
f =
function_handle with value:
  @(fr)(50*fr(1)^2+100)/fr(1)+(175*fr(2)^2+150)/fr(2)+(160*fr(3)^2+250)/fr(3)
Local minimum possible. Constraints satisfied.
fmincon stopped because the size of the current step is less than
the default value of the step size tolerance and constraints are 
satisfied to within the default value of the constraint tolerance.
<stopping criteria details>
fr =
  1.4142    0.9258    1.2500
I want to find positive integer values rather than decimal values for my variables. is there any way to include this condition with fmincon? any help will be highly appreciated. thank you

Best Answer

fmincon is not designed to deal with integer x values. You should try ga() which has an IntCon option or patternsearch() with a round() on the input values.
Of course for a small problem like this there are only 216 unique combinations of x so you could easily brute force it.
[rr,cc,pp] = ndgrid(0:5);
v = (50*rr.^2 + 100)./rr + (175*cc.^2 + 150)./cc + (160*pp.^2 + 250)./pp;
[val, idx] = min(v(:));
[rr(idx) cc(idx) pp(idx)]
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