Converting MultivariatePolynomials output as a function to be used in JuMP

Specific Domains Optimization (Mathematical)
1

The objective is to solve a large system of NL equations. Equations should be obtained via polynomial operations and passed on to JuMP as user-defined function. Below is the minuaturised code for eveluating polynomials’ variables as function’s arguments:
using JuMP
using Ipopt
using MultivariatePolynomials
using DynamicPolynomials
function f(k_1,c_1)
c_1*k_1^2
end
@polyvar c_1 k_1 s
d=2*k_1^2+c_1-s
p5=subs(d,s=>f(k_1,c_1))
function y_2(c,k)
p5(c_1=>c,k_1=>k)
end
y_2(c,k)
The error message is the following when I call for the evaluated function:
UndefVarError: c not defined

Please, what is wrong in the code? How differently can I convert MultivariatePolynomials output into user-defined functions usable into JuMP?

2

The variables c and k do not have any value in your code.
You get the same error if you do

function y_2(c, k)
    c + y
end
y_2(c, k)

What do you intend to do with the line y_2(c, k) ?

3

y_2(c,k) is going to be used as user-defined function in JuMP with c and k the unknowns of the non-linear system to be solved.

4

When I register y_2(c,k) as a user defined function in the real model, I receive the following error:

  `AssertionError: Variable c_1 was not assigned a value`

  `Stacktrace:`
  
 `[1]_subsmap(::MultivariatePolynomials.Eval,::Array{DynamicPolynomials.PolyVar{true},1},::Tuple{Pair{DynamicPolynomials.PolyVar{true},Float64},`
  `Pair{DynamicPolynomials.PolyVar{true},Float64},Pair{DynamicPolynomials.PolyVar{true},Float64},Pair{DynamicPolynomials.PolyVar{true},Float64},Pair{DynamicPolynomials.PolyVar{true},Float64},.....`

Thanks for your help

5

It is difficult to tell you what is the issue without a minimal working example but it could be cause by calling @polyvar twice. Indeed, in DynamicPolynomials, the equality between variables is not based on the name, each variable is different. For instance,

using JuMP
using Ipopt
using MultivariatePolynomials
using DynamicPolynomials
function f(k_1,c_1)
    c_1*k_1^2
end
@polyvar c_1 k_1 s
d=2*k_1^2+c_1-s
p5=subs(d,s=>f(k_1,c_1))
@polyvar c_1
function y_3(c,k)
    p5(c_1=>c,k_1=>k)
end
m = Model()
@variable m c
@variable m k
y_3(c, k)

throws the error AssertionError: Variable c_1 was not assigned a value because the c_1 using in p5(c_1=>c,k_1=>k) is different than the c_1 used in d=2*k_1^2+c_1-s and p5=subs(d,s=>f(k_1,c_1)).

6

I have just added a notebook detailing how to solve polynomial optimization here that might be helpful.

2 Likes
7

Thanks a lot! Going to have a look now.

8

I ran
Pkg.build()
and no error message related to the conversion of MultivariatePolynomials output to a function anymore.

Thanks for your help.

1 Like