Confusing error message in nonlinear

[odow]

Reported on slack:

julia> using JuMP, Ipopt, LinearAlgebra

julia> model = Model(Ipopt.Optimizer)
A JuMP Model
Feasibility problem with:
Variables: 0
Model mode: AUTOMATIC
CachingOptimizer state: EMPTY_OPTIMIZER
Solver name: Ipopt

julia> @variable(model, K[1:2,1:5])
2×5 Matrix{VariableRef}:
 K[1,1]  K[1,2]  K[1,3]  K[1,4]  K[1,5]
 K[2,1]  K[2,2]  K[2,3]  K[2,4]  K[2,5]

julia> A, B = rand(5, 5), rand(5, 2)
([0.8069977376091964 0.6161158349878504 … 0.46291003291226973 0.6360012232068746; 0.52213926623547 0.9495143399637247 … 0.07360503427198917 0.4978696526920816; … ; 0.14586717136824756 0.0003306031458678582 … 0.5010140965992376 0.4367748246176837; 0.4658645107067667 0.6366232080273633 … 0.4371067511526787 0.17266344404530498], [0.671429492429769 0.8062021626377329; 0.31489671797256236 0.02573618075020523; … ; 0.23639100794402879 0.7547242181976781; 0.7930804839731864 0.8228698868125954])

julia> @NLobjective(model, Min, sum(abs.(eigvals(A+B*K))))
ERROR: sqrt is not defined for type GenericQuadExpr. Are you trying to build a nonlinear problem? Make sure you use @NLconstraint/@NLobjective.
Stacktrace:
 [1] error(s::String)
   @ Base ./error.jl:33
 [2] sqrt(#unused#::QuadExpr)
   @ JuMP ~/.julia/packages/JuMP/bofhg/src/operators.jl:472
 [3] eigtype(T::Type)
   @ LinearAlgebra /Users/julia/buildbot/worker/package_macos64/build/usr/share/julia/stdlib/v1.6/LinearAlgebra/src/eigen.jl:302
 [4] eigvals(A::Matrix{AffExpr}; kws::Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
   @ LinearAlgebra /Users/julia/buildbot/worker/package_macos64/build/usr/share/julia/stdlib/v1.6/LinearAlgebra/src/eigen.jl:326
 [5] eigvals(A::Matrix{AffExpr})
   @ LinearAlgebra /Users/julia/buildbot/worker/package_macos64/build/usr/share/julia/stdlib/v1.6/LinearAlgebra/src/eigen.jl:326
 [6] macro expansion
   @ ~/.julia/packages/JuMP/bofhg/src/macros.jl:1867 [inlined]
 [7] top-level scope
   @ REPL[43]:1

The issue is that we try to eagerly evaluate the contents inside sum:

julia> @macroexpand @NLobjective(model, Min, sum(abs.(eigvals(A+B*K))))
quote
    #= REPL[44]:1 =#
    JuMP._valid_model(model, :model)
    begin
        #= /Users/oscar/.julia/packages/JuMP/bofhg/src/macros.jl:2390 =#
        begin
            #= /Users/oscar/.julia/packages/JuMP/bofhg/src/macros.jl:1867 =#
            JuMP._init_NLP(model)
            var"#24###309" = JuMP.Expr(:call, :sum, abs.(eigvals(A + B * K)))
            var"#25###310" = model.nlp_model.operators
            begin
                #= /Users/oscar/.julia/packages/JuMP/bofhg/src/macros.jl:1911 =#
                try
                    #= /Users/oscar/.julia/packages/JuMP/bofhg/src/macros.jl:1912 =#
                    (JuMP.MOI).Nonlinear.register_operator_if_needed(var"#25###310", :sum, 1, sum)
                catch
                end
                #= /Users/oscar/.julia/packages/JuMP/bofhg/src/macros.jl:1920 =#
                (JuMP.MOI).Nonlinear.assert_registered(var"#25###310", :sum, 1)
            end
        end
        #= /Users/oscar/.julia/packages/JuMP/bofhg/src/macros.jl:2391 =#
        JuMP.set_nonlinear_objective(model, JuMP._throw_error_for_invalid_sense(JuMP.var"#_error#97"{LineNumberNode, Symbol, Symbol, Expr}(:(#= REPL[44]:1 =#), :model, :Min, :(sum(abs.(eigvals(A + B * K))))), MathOptInterface.MIN_SENSE), var"#24###309")
    end
end

[odow]

MWE:

julia> using JuMP

julia> model = Model();

julia> @variable(model, x[1:2]);

julia> @NLobjective(model, Min, sum(sin.(x)))
ERROR: sin is not defined for type AbstractVariableRef. Are you trying to build a nonlinear problem? Make sure you use @NLconstraint/@NLobjective.
Stacktrace:
 [1] error(s::String)
   @ Base ./error.jl:33
 [2] sin(#unused#::VariableRef)
   @ JuMP ~/.julia/dev/JuMP/src/operators.jl:472
 [3] _broadcast_getindex_evalf
   @ ./broadcast.jl:648 [inlined]
 [4] _broadcast_getindex
   @ ./broadcast.jl:621 [inlined]
 [5] getindex
   @ ./broadcast.jl:575 [inlined]
 [6] copy
   @ ./broadcast.jl:922 [inlined]
 [7] materialize(bc::Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Nothing, typeof(sin), Tuple{Vector{VariableRef}}})
   @ Base.Broadcast ./broadcast.jl:883
 [8] macro expansion
   @ ~/.julia/dev/JuMP/src/macros.jl:1867 [inlined]
 [9] top-level scope
   @ REPL[24]:1

[odow]

So the issue is the broadcast sin.(. It's likely been an issue in JuMP forever. Here's v1.0.0 (prior to the nonlinear changes)

(jmp) pkg> st
      Status `/private/tmp/jmp/Project.toml`
  [4076af6c] JuMP v1.0.0

julia> using JuMP

julia> model = Model();

julia> @variable(model, x[1:2]);

julia> @NLobjective(model, Min, sum(sin.(x)))
ERROR: sum() can appear in nonlinear expressions  only if the argument is a generator statement, for example, sum(x[i] for i in 1:N).
Stacktrace:
 [1] error(s::String)
   @ Base ./error.jl:33
 [2] macro expansion
   @ ~/.julia/packages/JuMP/0C6kd/src/parse_nlp.jl:544 [inlined]
 [3] macro expansion
   @ ~/.julia/packages/JuMP/0C6kd/src/macros.jl:2057 [inlined]
 [4] top-level scope
   @ REPL[17]:1

julia> @NLobjective(model, Min, sin.(x)' * (1:2))
ERROR: sin is not defined for type AbstractVariableRef. Are you trying to build a nonlinear problem? Make sure you use @NLconstraint/@NLobjective.
Stacktrace:
  [1] error(s::String)
    @ Base ./error.jl:33
  [2] sin(#unused#::VariableRef)
    @ JuMP ~/.julia/packages/JuMP/0C6kd/src/operators.jl:409
  [3] _broadcast_getindex_evalf
    @ ./broadcast.jl:648 [inlined]
  [4] _broadcast_getindex
    @ ./broadcast.jl:621 [inlined]
  [5] getindex
    @ ./broadcast.jl:575 [inlined]
  [6] copy
    @ ./broadcast.jl:922 [inlined]
  [7] materialize(bc::Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Nothing, typeof(sin), Tuple{Vector{VariableRef}}})
    @ Base.Broadcast ./broadcast.jl:883
  [8] macro expansion
    @ ~/.julia/packages/JuMP/0C6kd/src/parse_nlp.jl:544 [inlined]
  [9] macro expansion
    @ ~/.julia/packages/JuMP/0C6kd/src/macros.jl:2057 [inlined]
 [10] top-level scope
    @ REPL[18]:1

[odow]

This is actually quite hard to fix, because we currently support things like:

using JuMP
model = Model();
@variable(model, x);
a = 1
@NLobjective(model, Min, x * sin.(a))

In this case, we eagerly evaluate sin.(a), which, despite being a broadcast, returns a scalar:

julia> @macroexpand @NLobjective(model, Min, x * sin.(a))
quote
    #= REPL[51]:1 =#
    JuMP._valid_model(model, :model)
    begin
        #= /Users/oscar/.julia/dev/JuMP/src/macros.jl:2390 =#
        begin
            #= /Users/oscar/.julia/dev/JuMP/src/macros.jl:1867 =#
            JuMP._init_NLP(model)
            var"#121###337" = JuMP.Expr(:call, :*, x, sin.(a))
        end
        #= /Users/oscar/.julia/dev/JuMP/src/macros.jl:2391 =#
        JuMP.set_nonlinear_objective(model, JuMP._throw_error_for_invalid_sense(JuMP.var"#_error#97"{LineNumberNode, Symbol, Symbol, Expr}(:(#= REPL[51]:1 =#), :model, :Min, :(x * sin.(a))), MathOptInterface.MIN_SENSE), var"#121###337")
    end
end

So it's breaking to now disallow all broadcasts. We could potentially check if any of the arguments to a broadcast are variables. But that might also cause issues. Perhaps we just need to improve the error message.