Convergence detection for optimization algorithms: Approximate-KKT stopping criterion when Lagrange multipliers are not available

In this paper we investigate how to efficiently apply ApproximateKarush-Kuhn-Tucker (AKKT) proximity measures as stopping criteria for optimization algorithms that do not generate approximations to Lagrange multipliers, in particular, Genetic Algorithms. We prove that for a wide range of constrained optimization problems the KKT error measurement tends to zero. We also develop a simple model to compute the KKT error measure requiring only the solution of a non-negative linear least squares problem. Our numerical experiments show the efficiency of the strategy.