Add unbounded objective tests (#268)

* add unbounded below obj test. Fix unbounded test in fomo.

* add unbounded below obj test. Fix unbounded test in fomo.

* standardize fomo :unbounded condition,
add objective value test in unbounded tests.

* rename: fk -> f0

src/fomo.jl

@@ -279,7 +279,8 @@ function SolverCore.solve!(
   d = use_momentum ? solver.d : solver.g # g = d if no momentum
   p = use_momentum ? solver.p : nothing # not used if no momentum
   set_iter!(stats, 0)
-  set_objective!(stats, obj(nlp, x))
+  f0 = obj(nlp, x)
+  set_objective!(stats, f0)
 
   grad!(nlp, x, ∇fk)
   norm_∇fk = norm(∇fk)
@@ -288,6 +289,9 @@ function SolverCore.solve!(
   solver.α = init_alpha(norm_∇fk, step_backend)
 
   # Stopping criterion: 
+  fmin = min(-one(T), f0) / eps(T)
+  unbounded = f0 < fmin
+
   ϵ = atol + rtol * norm_∇fk
   optimal = norm_∇fk ≤ ϵ
   step_param_name = is_r2 ? "σ" : "Δ"
@@ -321,6 +325,7 @@ function SolverCore.solve!(
       nlp,
       elapsed_time = stats.elapsed_time,
       optimal = optimal,
+      unbounded = unbounded,
       max_eval = max_eval,
       iter = stats.iter,
       max_iter = max_iter,
@@ -346,10 +351,7 @@ function SolverCore.solve!(
     step_underflow = x == c # step addition underfow on every dimensions, should happen before solver.α == 0
     ΔTk = ((oneT - βmax) * norm_∇fk^2 + βmax * mdot∇f) * λk # = dot(d,∇fk) * λk with momentum, ‖∇fk‖²λk without momentum
     fck = obj(nlp, c)
-    if fck == -Inf
-      set_status!(stats, :unbounded)
-      break
-    end
+    unbounded = fck < fmin
     ρk = (stats.objective - fck) / ΔTk
     # Update regularization parameters
     if ρk >= η2
@@ -406,6 +408,7 @@ function SolverCore.solve!(
         nlp,
         elapsed_time = stats.elapsed_time,
         optimal = optimal,
+        unbounded = unbounded,
         max_eval = max_eval,
         iter = stats.iter,
         max_iter = max_iter,

test/runtests.jl

@@ -35,6 +35,19 @@ end
   end
 end
 
+@testset "Test unbounded below" begin
+  @testset "$fun" for fun in (R2, fomo, lbfgs, tron, trunk)
+    T = Float64
+    x0 = [T(0)]
+    f(x) = -exp(x[1])
+    nlp = ADNLPModel(f, x0)
+
+    stats = eval(fun)(nlp)
+    @test stats.status == :unbounded
+    @test stats.objective < -one(T)/eps(T)
+  end
+end
+
 include("restart.jl")
 include("callback.jl")
 include("consistency.jl")