add improper check and return in R2N & R2DH

Author: MaxenceGollier

src/R2DH.jl

@@ -115,7 +115,7 @@ For advanced usage, first define a solver "R2DHSolver" to preallocate the memory
 - `η2::T = T(0.9)`: successful iteration threshold;
 - `ν::T = eps(T)^(1 / 5)`: inverse of the initial regularization parameter: ν = 1/σ;
 - `γ::T = T(3)`: regularization parameter multiplier, σ := σ/γ when the iteration is very successful and σ := σγ when the iteration is unsuccessful.
-- `θ::T = eps(T)^(1/5)`: is the model decrease fraction with respect to the decrease of the Cauchy model. 
+- `θ::T = 1/(1 + eps(T)^(1 / 5))`: is the model decrease fraction with respect to the decrease of the Cauchy model. 
 - `m_monotone::Int = 6`: monotoneness parameter. By default, R2DH is non-monotone but the monotone variant can be used with `m_monotone = 1`
 
 The algorithm stops either when `√(ξₖ/νₖ) < atol + rtol*√(ξ₀/ν₀) ` or `ξₖ < 0` and `√(-ξₖ/νₖ) < neg_tol` where ξₖ := f(xₖ) + h(xₖ) - φ(sₖ; xₖ) - ψ(sₖ; xₖ), and √(ξₖ/νₖ) is a stationarity measure.
@@ -245,6 +245,8 @@ function SolverCore.solve!(
     verbose > 0 && @debug "R2DH: found point where h has value" hk
   end
   improper = (hk == -Inf)
+  improper == true && @warn "R2DH: Improper term detected"
+  improper == true && return stats
 
   if verbose > 0
     @info log_header(

src/R2N.jl

@@ -256,6 +256,8 @@ function SolverCore.solve!(
     verbose > 0 && @debug "R2N: found point where h has value" hk
   end
   improper = (hk == -Inf)
+  improper == true && @warn "R2N: Improper term detected"
+  improper == true && return stats
 
   if verbose > 0
     @info log_header(