A New Sequential Optimality Condition for Constrained Optimization and Algorithmic Consequences

Necessary first-order sequential optimality conditions provide adequate theoretical tools to justify stopping criteria for nonlinear programming solvers. Sequential optimality conditions are satisfied by local minimizers of optimization problems independently of the fulfillment of constraint qualifications. A new condition of this type is introduced in the present paper. It will be proved that a well established Augmented Lagrangian algorithm produces sequences whose limits satisfy the new condition. Practical consequences will be discussed.