Registering an array of functions and using them in constraints and objectives

Specific Domains Optimization (Mathematical)
#1

(Julia beginner)
Still thinking about Nonlinear Programming with JuMP with some generality.
(@NLconstraint with a sum, array and scalar variables)
There are many NLP JuMP examples available but all more or less similar to the Rosenbrok problem in the sense that they involve a few explicit functions for objective and constraints.

My intuition for my own problem (pyro chemistry) is that I might need to create many nonlinear functions and that I would use as part of an array of functions or a dictionary of functions.
Therefore when registering some new function(s) with some symbol(s) like here:

JuMP.register(model, :hJuMP, 1, hjulia; autodiff=true)

there is the problem that I will probably never be able to use literally the hJuMP symbol created in this statement. Instead, my likely use of hJuMP would be as one element from a list of such function:

funlist = [..., ..., hJuMP, ..., ...]

@NLconstraint(model, funlist[idx](T, xs...) ==  h0)

This kind of statement does not work and return for example this error:

LoadError: MethodError: no method matching _is_sum(::Expr)

I tried several variant of the idea without success.

Would there be a way to use JuMP/Julia as above?
Or should I think otherwise?

Thanks for your suggestions,

Michel

#2

This may help:

using JuMP, Ipopt

function main(functions)
    model = Model(Ipopt.Optimizer)
    @variable(model, x)
    for (i, f) in enumerate(functions)
        f_sym = Symbol("f_$(i)")
        register(model, f_sym, 1, f; autodiff = true)
        add_NL_constraint(model, :($(f_sym)($x) <= 1.0))
    end
    return model
end

main([
    x -> x^2,
    x -> sin(x)^2,
])

I should add it as an example to the documentation. The current section on this is a little bare: Nonlinear Modeling · JuMP

1 Like
Optimization with JuMP: an affine expression enters a nonlinear constraint (dynamic discrete choice)
#3

Thanks odow, it could help indeed …

How would you modify the last line of this snippet to involve a sum() on these two functions ?


model = Model(Ipopt.Optimizer)
f_sym = [:f_1, :f_2]
f_fun = [x -> x^2, x -> sin(x)^2]
@variable(model, x)
for (s, f) in zip(f_sym,f_fun)
    register(model, s, 1, f; autodiff = true)
end
#@NLconstraint(model, f_1(x) + f_2(x) <= 1.0 )
add_NL_constraint(model, :($(f_sym[1])($x) + $(f_sym[2])($x) <= 1.0) )

As a beginner, I get already confused when trying to adjust this (very) naïve attempt:

add_NL_constraint(model, :( sum( $(f_sym[i])($x) for i in 1:2) <= 1.0) )

or this variant:

add_NL_constraint(model, :( sum( (($f)($x)) for f in f_sym) <= 1.0) )

Could you also suggest some readings on metaprogramming that deal with this kind of yoga with expressions? Explaining the mechanics of it a bit more in detail than what I found already.

Thanks!

1 Like
#4

You need to build the expression manually:

expr = Expr(:call, :+)
for f in f_sym
    push!(expr.args, :($(f)($x))
end
add_NL_constraint(model, :($(expr) <= 1.0) )

Here are the Julia docs: Metaprogramming · The Julia Language

It’s often helpful to write the expression you want to achieve, then dump it to see the internal structure:

julia> expr = :(f_1(x) + f_2(x) <= 1)
:(f_1(x) + f_2(x) <= 1)

julia> dump(expr)
Expr
  head: Symbol call
  args: Array{Any}((3,))
    1: Symbol <=
    2: Expr
      head: Symbol call
      args: Array{Any}((3,))
        1: Symbol +
        2: Expr
          head: Symbol call
          args: Array{Any}((2,))
            1: Symbol f_1
            2: Symbol x
        3: Expr
          head: Symbol call
          args: Array{Any}((2,))
            1: Symbol f_2
            2: Symbol x
    3: Int64 1
#5

Thanks odow!