diff --git a/src/R2_alg.jl b/src/R2_alg.jl
index 91c54543..4d9ba7b4 100644
--- a/src/R2_alg.jl
+++ b/src/R2_alg.jl
@@ -69,12 +69,13 @@ function R2(
   f::F,
   ∇f!::G,
   h::H,
-  options::ROSolverOptions,
-  x0::AbstractVector,
-) where {F <: Function, G <: Function, H}
+  options::ROSolverOptions{R},
+  x0::AbstractVector{R},
+) where {F <: Function, G <: Function, H, R <: Real}
   start_time = time()
   elapsed_time = 0.0
   ϵ = options.ϵ
+  neg_tol = options.neg_tol
   verbose = options.verbose
   maxIter = options.maxIter
   maxTime = options.maxTime
@@ -146,13 +147,13 @@ function R2(
     Complex_hist[k] += 1
     mks = mk(s)
     ξ = hk - mks + max(1, abs(hk)) * 10 * eps()
-    ξ > 0 || error("R2: prox-gradient step should produce a decrease but ξ = $(ξ)")
-
-    if sqrt(ξ) < ϵ
+    
+    if (ξ < 0 && sqrt(-ξ) ≤ -neg_tol) || (ξ ≥ 0 && sqrt(ξ) ≤ ϵ)
       optimal = true
       continue
     end
 
+    ξ > 0 || error("R2: prox-gradient step should produce a decrease but ξ = $(ξ)")
     xkn .= xk .+ s
     fkn = f(xkn)
     hkn = h(xkn)
diff --git a/src/input_struct.jl b/src/input_struct.jl
index 56e94663..a111065f 100644
--- a/src/input_struct.jl
+++ b/src/input_struct.jl
@@ -2,6 +2,7 @@ export ROSolverOptions
 
 mutable struct ROSolverOptions{R}
   ϵ::R  # termination criteria
+  neg_tol::R # tolerance when ξ < 0
   Δk::R  # trust region radius
   verbose::Int  # print every so often
   maxIter::Int  # maximum amount of inner iterations
@@ -17,6 +18,7 @@ mutable struct ROSolverOptions{R}
 
   function ROSolverOptions{R}(;
     ϵ::R = √eps(R),
+    neg_tol::R = eps(R)^(1 / 3),
     Δk::R = one(R),
     verbose::Int = 0,
     maxIter::Int = 10000,
@@ -26,11 +28,24 @@ mutable struct ROSolverOptions{R}
     η2::R = R(0.9),
     α::R = 1 / eps(R),
     ν::R = 1.0e-3,
-    γ::R = R(3.0),
+    γ::R = R(3),
     θ::R = R(1e-3),
-    β::R = R(10.0),
+    β::R = R(10),
   ) where {R <: Real}
-    return new{R}(ϵ, Δk, verbose, maxIter, maxTime, σmin, η1, η2, α, ν, γ, θ, β)
+    @assert ϵ ≥ 0
+    @assert neg_tol ≥ 0
+    @assert Δk > 0
+    @assert verbose ≥ 0
+    @assert maxIter ≥ 0
+    @assert maxTime ≥ 0
+    @assert σmin ≥ 0
+    @assert 0 < η1 < η2 < 1
+    @assert α > 0
+    @assert ν > 0
+    @assert γ > 1
+    @assert θ > 0
+    @assert β ≥ 1
+    return new{R}(ϵ, neg_tol, Δk, verbose, maxIter, maxTime, σmin, η1, η2, α, ν, γ, θ, β)
   end
 end