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. These conditions are satisfied by local minimizers of optimization problems independently of the fulfillment of constraint qualifications. 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. Key words: Nonlinear Programming, Optimality Conditions, Approximate KKT conditions, Stopping criteria. AMS Subject Classification: 90C30, 49K99, 65K05.

• Type: Journal
• Year: 2010
• Where: SIAMJO
• Authors: Roberto Andreani, José Mario Martínez, Benar Fux Svaiter
• Keywords: Nonlinear Programming, Optimality Conditions, Sequential Optimality Condition, SIAMJO 2010