JuMP: AffExpr error

Specific Domains Optimization (Mathematical)
1

I’m using Julia v0.6.4 on Ubuntu (14.04) and am getting an affine expression error in the following toy model:

using JuMP
using Ipopt

model = Model(solver=IpoptSolver())

## params
N = 5
idx1 = [1, 2]
idx2 = [5, 4]

## variables
@variable(model, x_r[1:N])
@variable(model, x_i[1:N])

## constraints
for i = 1:length(idx1)
    j = idx1[i]
    k = idx2[i]
    ## below I want: 2 * (x_r[j] - x_r[k])^2 +  2 * (x_i[j] - x_i[k])^2 - 1 >= 0.0
    ae_r = AffExpr([x_r[j], x_r[k]], [1.0, -1.0])  ## <<-- ERROR
    ae_i = AffExpr([x_i[j], x_i[k]], [1.0, -1.0])
    @NLexpression(model, nle[i], 2.0 * (ae_r^2 + ae_i^2))
    @NLconstraint(model, nle[i] - 1.0 >= 0.0)
end

the error is:

ERROR: MethodError: no method matching JuMP.GenericAffExpr{Float64,JuMP.Variable}(::Array{JuMP.Variable,1}, ::Array{Float64,1})
Stacktrace:
 [1] macro expansion at ./REPL[145]:5 [inlined]
 [2] anonymous at ./<missing>:?

I looked at the docs but am confused about what I’m doing wrong. I tried with the following adjustment:

ae_r = AffExpr([x_r[j], x_r[k]], [1.0, -1.0], 0.0)
ae_i = AffExpr([x_i[j], x_i[k]], [1.0, -1.0], 0.0)

and received the error:

ERROR: MethodError: no method matching parseNLExpr_runtime(::JuMP.Model, ::JuMP.GenericAffExpr{Float64,JuMP.Variable}, ::Array{ReverseDiffSparse.NodeData,1}, ::Int64, ::Array{Float64,1})
Closest candidates are:
  parseNLExpr_runtime(::JuMP.Model, ::Number, ::Any, ::Any, ::Any) at /homes/jmroth/.julia/v0.6/JuMP/src/parsenlp.jl:196
  parseNLExpr_runtime(::JuMP.Model, ::JuMP.Variable, ::Any, ::Any, ::Any) at /homes/jmroth/.julia/v0.6/JuMP/src/parsenlp.jl:202
  parseNLExpr_runtime(::JuMP.Model, ::JuMP.NonlinearExpression, ::Any, ::Any, ::Any) at /homes/jmroth/.julia/v0.6/JuMP/src/parsenlp.jl:208
  ...
Stacktrace:
 [1] macro expansion at /homes/USER/.julia/v0.6/JuMP/src/parsenlp.jl:226 [inlined]
 [2] macro expansion at /homes/USER/.julia/v0.6/JuMP/src/macros.jl:1264 [inlined]
 [3] macro expansion at ./REPL[154]:7 [inlined]
 [4] anonymous at ./<missing>:?

Any help would be appreciated! Thanks!

2

I think I had an error with using @NL. Will update later tonight.

Update: Can’t build a QuadExpr from AffExpr. Should have just used QuadExpr from the beginning.

3

See the syntax notes for nonlinear modelling in the JuMP docs.

AffExpr and QuadExpr objects cannot currently be used inside nonlinear expressions. Instead,
introduce auxiliary variables, e.g.:

myexpr = dot(c,x) + 3y # where x and y are variables
@variable(m, aux)
@constraint(m, aux == myexpr)
@NLobjective(m, Min, sin(aux))

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