Necessary first-order sequential optimality conditions provide adequate theoretical tools to justify stopping criteria for nonlinear programming solvers. These conditions are satisfied by local minimizers of optimization problems independently of the fulfillment of constraint qual- i cations. A new strong sequential optimality condition is introduced in the present paper. A proof that a well established Augmented Lagrangian algorithm produces sequences whose limits satisfy the new condition is given. Practical consequences will be discussed.
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View A new sequential optimality condition for constrained optimization and algorithmic consequences