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

In this paper we investigate how to efficiently apply Approximate-Karush–Kuhn–Tucker proximity measures as stopping criteria for optimization algorithms that do not generate approximations to Lagrange multipliers. We prove that the KKT error measurement tends to zero when approaching a solution and we 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 on a Genetic Algorithm show the efficiency of the strategy.