diff --git a/src/AL_alg.jl b/src/AL_alg.jl
index ef652c26..6d3f3fb6 100644
--- a/src/AL_alg.jl
+++ b/src/AL_alg.jl
@@ -155,7 +155,7 @@ function ALSolver(reg_nlp::AbstractRegularizedNLPModel{T, V}; kwargs...) where {
   cx = V(undef, ncon)
   y = V(undef, ncon)
   has_bnds = has_bounds(nlp)
-  sub_model = AugLagModel(nlp, V(undef, ncon), T(0), x, T(0), V(undef, ncon))
+  sub_model = AugLagModel(nlp, V(undef, ncon), T(0), x, T(0), cx)
   sub_problem = RegularizedNLPModel(sub_model, reg_nlp.h, reg_nlp.selected)
   sub_solver = R2Solver(reg_nlp; kwargs...)
   sub_stats = RegularizedExecutionStats(sub_problem)
diff --git a/src/R2N.jl b/src/R2N.jl
index e1304725..75cd16c7 100644
--- a/src/R2N.jl
+++ b/src/R2N.jl
@@ -134,7 +134,7 @@ For advanced usage, first define a solver "R2NSolver" to preallocate the memory
 - `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 = 1/(1 + eps(T)^(1 / 5))`: is the model decrease fraction with respect to the decrease of the Cauchy model;
 - `m_monotone::Int = 1`: monotonicity parameter. By default, R2N is monotone but the non-monotone variant will be used if `m_monotone > 1`;
-- `sub_kwargs::Dict{Symbol}`: a dictionary containing the keyword arguments to be sent to the subsolver. The solver will fail if invalid keyword arguments are provided to the subsolver.
+- `sub_kwargs::NamedTuple = NamedTuple()`: a named tuple containing the keyword arguments to be sent to the subsolver. The solver will fail if invalid keyword arguments are provided to the subsolver. For example, if the subsolver is `R2Solver`, you can pass `sub_kwargs = (max_iter = 100, σmin = 1e-6,)`.
 
 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.
 
@@ -174,7 +174,7 @@ function R2N(
   selected = pop!(kwargs_dict, :selected, 1:(nlp.meta.nvar))
   x0 = pop!(kwargs_dict, :x0, nlp.meta.x0)
   reg_nlp = RegularizedNLPModel(nlp, h, selected)
-  sub_kwargs = pop!(kwargs_dict, :sub_kwargs, Dict{Symbol, Any}())
+  sub_kwargs = pop!(kwargs_dict, :sub_kwargs, NamedTuple())
   return R2N(
     reg_nlp,
     x = x0,
@@ -226,7 +226,7 @@ function SolverCore.solve!(
   γ::T = T(3),
   β::T = 1 / eps(T),
   θ::T = 1/(1 + eps(T)^(1 / 5)),
-  sub_kwargs::Dict{Symbol} = Dict(),
+  sub_kwargs::NamedTuple = NamedTuple(),
 ) where {T, V, G}
   reset!(stats)
 
@@ -365,11 +365,11 @@ function SolverCore.solve!(
     solver.subpb.model.σ = σk
     isa(solver.subsolver, R2DHSolver) && (solver.subsolver.D.d[1] = 1/ν₁)
     if isa(solver.subsolver, R2Solver) #FIXME
-      sub_kwargs[:ν] = ν₁
+      solve!(solver.subsolver, solver.subpb, solver.substats; x = s1, ν = ν₁, atol = sub_atol, sub_kwargs...)
     else
-      sub_kwargs[:σk] = σk
+      solve!(solver.subsolver, solver.subpb, solver.substats; x = s1, σk = σk, atol = sub_atol, sub_kwargs...)
     end
-    solve!(solver.subsolver, solver.subpb, solver.substats; x = s1, atol = sub_atol, sub_kwargs...)
+    
 
     s .= solver.substats.solution
 
diff --git a/src/TR_alg.jl b/src/TR_alg.jl
index e53b7f89..631a62e7 100644
--- a/src/TR_alg.jl
+++ b/src/TR_alg.jl
@@ -131,6 +131,7 @@ For advanced usage, first define a solver "TRSolver" to preallocate the memory u
 - `γ::T = T(3)`: trust-region radius parameter multiplier. Must satisfy `γ > 1`. The trust-region radius is updated as Δ := Δ*γ when the iteration is very successful and Δ := Δ/γ when the iteration is unsuccessful;
 - `χ::F =  NormLinf(1)`: norm used to define the trust-region;`
 - `subsolver::S = R2Solver`: subsolver used to solve the subproblem that appears at each iteration.
+- `sub_kwargs::NamedTuple = NamedTuple()`: a named tuple containing the keyword arguments to be sent to the subsolver. The solver will fail if invalid keyword arguments are provided to the subsolver. For example, if the subsolver is `R2Solver`, you can pass `sub_kwargs = (max_iter = 100, σmin = 1e-6,)`.
 
 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.
 
@@ -199,6 +200,7 @@ function SolverCore.solve!(
   η1::T = √√eps(T),
   η2::T = T(0.9),
   γ::T = T(3),
+  sub_kwargs::NamedTuple = NamedTuple(),
 ) where {T, G, V}
   reset!(stats)
 
@@ -353,6 +355,7 @@ function SolverCore.solve!(
           x = s,
           atol = stats.iter == 0 ? 1e-5 : max(sub_atol, min(1e-2, sqrt_ξ1_νInv)),
           Δk = ∆_effective / 10,
+          sub_kwargs...
         )
       else
         solve!(
@@ -362,6 +365,7 @@ function SolverCore.solve!(
           x = s,
           atol = stats.iter == 0 ? 1e-5 : max(sub_atol, min(1e-2, sqrt_ξ1_νInv)),
           ν = ν₁,
+          sub_kwargs...
         )
       end
     end