Abstract
This chapter presents a state-of-the-art survey for safeguarded augmented Lagrangian methods for constrained optimization problems in Banach spaces. The difference between the classical augmented Lagrangian method and its safeguarded version lies in the update of the multiplier estimates. The safeguarded method has significantly stronger global convergence properties than the classical algorithm. Local and rate-of-convergence results are also summarized. Some numerical results illustrate the practical behavior of the safeguarded augmented Lagrangian approach.
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