Executing R2N twice in a row does not give the same answer

[MaxenceGollier]

MRE

using LinearAlgebra: length
using LinearAlgebra, Random
using ProximalOperators

using NLPModels
using  NLPModelsModifiers, RegularizedProblems, RegularizedOptimization, SolverCore


Random.seed!(0)
compound = 1
bpdn, _, _ = bpdn_model(compound)
λ = norm(grad(bpdn, zeros(bpdn.meta.nvar)), Inf) / 10

h = NormL0(λ)

reg_nlp = RegularizedNLPModel(LBFGSModel(bpdn), h)
solver = R2NSolver(reg_nlp)
stats = RegularizedExecutionStats(reg_nlp)

solve!(solver, reg_nlp, stats, σk = 1.0, atol = 1e-6, rtol = 1e-6)
println(stats.solver_specific[:sigma_cauchy])
solve!(solver, reg_nlp, stats, σk = 1.0, atol = 1e-6, rtol = 1e-6)
println(stats.solver_specific[:sigma_cauchy])

results in

2.220069341990324
3.242917504053576

This is due to the v0 entry not being reset to its original value at the start.