# PolyJuMP: constraints on an arbitrarily large multinomial

**URL:** <https://discourse.julialang.org/t/polyjump-constraints-on-an-arbitrarily-large-multinomial/74479>\
**Category:** Optimization (Mathematical)\
**Created:** [January 12, 2022, 11:49am UTC](https://discourse.julialang.org/t/polyjump-constraints-on-an-arbitrarily-large-multinomial/74479 "2022-01-12T11:49:04Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![jnlindsay](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jnlindsay/32/32706_2.png) [@jnlindsay](https://discourse.julialang.org/u/jnlindsay)\
**Post date:** [January 12, 2022, 11:49am UTC](https://discourse.julialang.org/t/polyjump-constraints-on-an-arbitrarily-large-multinomial/74479/1 "2022-01-12T11:49:04Z")

</div>

Hi everyone!

In using `DynamicPolynomials`, `SumOfSquares`, and `CSDP`, I have set up my objective function and constraints like so:

```julia
m = 2

@polyvar x[1:m]
p = x[1]^2 + x[2]^2
S = @set x[1] >= 0 &&
         x[1] <= 1 &&
         x[2] <= 0 &&
         x[2] <= 1 &&
         sum(x) == 1

```

(This is from the documentation [Polynomial Optimization · SumOfSquares](https://jump.dev/SumOfSquares.jl/stable/generated/Polynomial%20Optimization/polynomial_optimization/))

This works fine for fixed m = 2, but I want to be able to `@set` my constraints for a multinomial in an arbitrary number of variables; I don’t want to type `x[i] >= 0 && x[i] <= 1` m times. How can I achieve this?

P.S. In my adventures I tried doing something like using `reduce(add, [x[i] >= 0 for i = 1:m])` where `add(a, b)` is defined as `a && b`, but that didn’t work.