In this work we present some applications of the Approximate-Karush-Kuhn-Tucker (AKKT) optimality condition. In contrast with the usual KKT condition, AKKT is a strong optimality condition regardless of constraint qualifications. When a very weak constraint qualification is present, AKKT implies the usual KKT condition. We have used the AKKT condition and others so-called Sequential Optimality Conditions to provide adequate stopping criteria for iterative solvers. The AKKT condition has also been used as a theoretical tool to provide new very weak constraint qualifications associated to the convergence of Augmented Lagrangian, Sequential Quadratic Programming, Interior Point and Inexact Restoration methods. When approximate Lagrange multipliers are not generated by the solver, we can also use AKKT to define a stopping criterion. This has been applied to a Genetic Algorithm framework.