LD_SLSQP does not terminate on NaN

[joehuchette]

using JuMP
using NLopt
m = Model(solver=NLoptSolver(algorithm=:LD_SLSQP))
@defVar(m, c[1:2] >= 0)
@addConstraint(m, sum(c) <= 2)
@setNLObjective(m, Max, (c[1] + 0.7*c[2])^0.5 - (0.7*c[2])^0.5 + (c[2] + 0.7*c[1])^0.5 - (0.7*c[1])^0.5)
solve(m)

This hangs for a while, and when I manually exit, I get

ERROR: InterruptException:
 in eval_g at /Users/huchette/.julia/v0.4/JuMP/src/nlp.jl:274
 in g_ineq at /Users/huchette/.julia/v0.4/NLopt/src/NLoptSolverInterface.jl:179
 in nlopt_vcallback_wrapper at /Users/huchette/.julia/v0.4/NLopt/src/NLopt.jl:469
 in optimize! at /Users/huchette/.julia/v0.4/NLopt/src/NLopt.jl:509
 in optimize! at /Users/huchette/.julia/v0.4/NLopt/src/NLoptSolverInterface.jl:203
 in solvenlp at /Users/huchette/.julia/v0.4/JuMP/src/nlp.jl:491
 in solve at /Users/huchette/.julia/v0.4/JuMP/src/solvers.jl:9

cc @mlubin

[stevengj]

Does the ~/.julia/NLopt/test/tutorial_jump.jl example work?

[joehuchette]

Yep, that one works great. MWE:

using JuMP, NLopt
m = Model(solver=NLoptSolver(algorithm=:LD_MMA)) # or :LD_SLSQP
@defVar(m, c >= 0)
@setNLObjective(m, Min, sqrt(c))
solve(m)

Edit: also,

using JuMP, NLopt
m = Model(solver=NLoptSolver(algorithm=:LD_MMA))
@defVar(m, 0 <= c <= 1)
@setNLObjective(m, Max, sqrt(c))
solve(m)

[stevengj]

What does "MWE" mean?

[joehuchette]

Minimal working example, sorry.

[mlubin]

The hang is apparently inside JuMP code, but doesn't occur when another solver like Ipopt is used. Pretty strange.

[mlubin]

It's not hanging, it's just iterating without converging.

[stevengj]

Which part is iterating?

[mlubin]

NLopt

[stevengj]

What are the termination criteria? I don't see any tolerances.

[odow]

Just confirming that this is still a problem

using JuMP
import NLopt
m = Model(NLopt.Optimizer)
set_optimizer_attribute(m, "algorithm", :LD_SLSQP)
@variable(m, c[1:2] >= 0)
@constraint(m, sum(c) <= 2)
@NLobjective(m, Max, (c[1] + 0.7*c[2])^0.5 - (0.7*c[2])^0.5 + (c[2] + 0.7*c[1])^0.5 - (0.7*c[1])^0.5)
optimize!(m)

Although you could set time limits or tolerances to exit earlier:

julia> using JuMP

julia> import NLopt

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

julia> set_optimizer_attribute(m, "algorithm", :LD_SLSQP)

julia> set_optimizer_attribute(m, "maxtime", 3.0)

julia> @variable(m, c[1:2] >= 0, start = 0)
2-element Vector{VariableRef}:
 c[1]
 c[2]

julia> @constraint(m, sum(c) <= 2)
c[1] + c[2] ≤ 2.0

julia> @NLobjective(m, Max, (c[1] + 0.7*c[2])^0.5 - (0.7*c[2])^0.5 + (c[2] + 0.7*c[1])^0.5 - (0.7*c[1])^0.5)

julia> @time optimize!(m)
  3.005593 seconds (14.77 M allocations: 676.120 MiB, 4.12% gc time, 0.18% compilation time)

julia> termination_status(m)
TIME_LIMIT::TerminationStatusCode = 12

[odow]

So the issue is that the derivatives aren't defined at the default starting point of 0.0.

It seems like for this algorithm NLopt just lets NaN accumulate and doesn't error. Should it? Or are there some algorithms that support NaN and can recover?

[odow]

@stevengj I'd appreciate your feedback on this issue. What is the expected behavior when functions or gradients return NaN?

I bumped into this during https://github.com/JuliaOpt/NLopt.jl/pull/239/files#diff-1c91bbf6e133c9ebca6c69381a02bb628595d0216a3a095e281ddba57d495b9cR236-R237

[odow]

It seems like this is a known issue with some algorithms. stevengj/nlopt#38

But it is intended behavior for others: stevengj/nlopt#279 (comment)

So perhaps we just close this issue and deal with the consequences. No one else has come along to comment in nearly 10 years.

[odow]

The conclusion of the monthly developer call is that we should close this issue because it is nearly 10 years old, and because it is a "feature" of the upstream library. We shouldn't intercept NaN calls in NLopt.jl. (I'll also file this away as related to jump-dev/JuMP.jl#3664. It'd be good to be able to evaluate starting points of nonlinear programs to detect feasibility, gradients, etc.)