# How to use NMinimize with a large scale of variables?

I can only write like this:

NMinimize[
{GoalFunction[graph, {x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12}],
cons[graph, {x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12}, 2500],
x1 > 0, x2 > 0, x3 > 0, x4 > 0, x5 > 0, x6 > 0, x7 > 0,
x8 > 0, x9 > 0, x10 > 0, x11 > 0, x12 > 0},
{x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12}
]


But when I have thousands of variables, how to use it?

• Are you asking how to automate the input of variables without having to type each one? Sep 10, 2016 at 8:05

If you can avoid it: You don't. Use FindMinimum with a good starting point, if you can. NMinimize usually gets horribly slow when the number of variables increases.

Regarding syntax, you can a simple trick (works for FindMinimum and NMinimize): Declare an array of variables like this:

xs = Array[x, 12]


Now xs contains 12 separate variables:

{x[1], x[2], x[3], x[4], x[5], x[6], x[7], x[8], x[9], x[10], x[11], x[12]}

and you can use xs instead of writing the same 12 variables again and again:

FindMinimum[
{GoalFunction[graph, xs], cons[graph, xs, 2500], Thread[xs > 0]},
xs]


This works well for small to medium sized problems (thousands of variables).

I would try to use:

Module[{x = x, n = 12, vars},
vars = ToExpression[ToString[x] <> ToString[#]] & /@ Range[n];
NMinimize[
Flatten@{GoalFunction[graph, vars], cons[graph, vars, 2500],