The chapter describes the algorithm SMALSE (semi-monotonic augmented Lagrangians for separable and equality constraints) and its variant SMALBE for bound and equality constraints. The main idea of the algorithms is to treat both sets of constraints separately. This approach enables us to use the ingredients of the algorithms of the previous chapters. We also consider the algorithm SMALSE-Mw for separable and equality constraints with a strong curvature of the feasible set boundary. We prove the convergence results that support the solving of large problems. We introduce the adaptive preconditioning for improving the convergence rate. Numerical experiments illustrate optimality and the effect of adaptive reorthogonalization.