JuMP Dot Product/Norm/NLobjective

Specific Domains Optimization (Mathematical)
1

I’ve run into a number of issues with quadratic objectives in JuMP. A simple example is:

m = Model(solver = CplexSolver())
@variable(m, w[1:10])
@expression(m, dotproduct, sum(w[i]*w[i] for i = 1:10))

If I try to make the dotproduct squared the objective with @objective(m, Min, dotproduct^2) I get an error

ERROR: *(::QuadExpr,::QuadExpr) is not defined. Are you trying to build a nonlinear problem? Make sure you use @NLconstraint/@NLobjective.
Stacktrace:
 [1] power_by_squaring(::JuMP.GenericQuadExpr{Float64,JuMP.Variable}, ::Int64) at ./intfuncs.jl:169
 [2] literal_pow(::Base.#^, ::JuMP.GenericQuadExpr{Float64,JuMP.Variable}, ::Type{Val{2}}) at ./intfuncs.jl:208
 [3] macro expansion at ./REPL.jl:97 [inlined]
 [4] (::Base.REPL.##1#2{Base.REPL.REPLBackend})() at ./event.jl:73

If I try it with @NLobjective(m, Min, dotproduct^2), I get the error

ERROR: MethodError: no method matching parseNLExpr_runtime(::JuMP.Model, ::JuMP.GenericQuadExpr{Float64,JuMP.Variable}, ::Array{ReverseDiffSparse.NodeData,1}, ::Int64, ::Array{Float64,1})
Closest candidates are:
  parseNLExpr_runtime(::JuMP.Model, !Matched::Number, ::Any, ::Any, ::Any) at /home/paul/.julia/v0.6/JuMP/src/parsenlp.jl:196
  parseNLExpr_runtime(::JuMP.Model, !Matched::JuMP.Variable, ::Any, ::Any, ::Any) at /home/paul/.julia/v0.6/JuMP/src/parsenlp.jl:202
  parseNLExpr_runtime(::JuMP.Model, !Matched::JuMP.NonlinearExpression, ::Any, ::Any, ::Any) at /home/paul/.julia/v0.6/JuMP/src/parsenlp.jl:208
  ...
Stacktrace:
 [1] macro expansion at ./REPL.jl:97 [inlined]
 [2] (::Base.REPL.##1#2{Base.REPL.REPLBackend})() at ./event.jl:73

Aren’t those the only two ways to add the objectives?

2

Could you try with @NLexpression and @NLobjective?

3

Note that you ought to also be able to just do w⋅w, though I’m not completely sure that @NLexpression and @NLobjective will cooperate with that.

4

I think your problem is that dotproduct^2 is not quadratic since dotproduct is quadratic.

5

It seemed to work with @NLexpression and @NLobjective

ExpandingMan: Yes, the dot product only works with the linear expression and objective right now which is why I had to write it the other way