Addressing the issue where $m_k(s_k) = - \infty$ in Regularized solvers

In this case, the solvers R2, R2N, R2DH, and LM should be able to increase $$\sigma_k$$ until the function becomes prox-friendly.

Ideally, we should avoid recomputing the objective and performing tests, as we already know that the iteration will inevitably be unsuccessful.