Abstract
In this paper, in order to obtain some existence results about solutions of the augmented Lagrangian problem for a constrained problem in which the objective function and constraint functions are noncoercive, we construct a new augmented Lagrangian function by using an auxiliary function. We establish a zero duality gap result and a sufficient condition of an exact penalization representation for the constrained problem without the coercive or level-bounded assumption on the objective function and constraint functions. By assuming that the sequence of multipliers is bounded, we obtain the existence of a global minimum and an asymptotically minimizing sequence for the constrained optimization problem.
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This work was supported by grants from Jiangsu Education Committee of China (No. 08KJB110009), the Research Grant Council of Hong Kong (PolyU 5334/08E) and Natural Science Foundation of China (11071180) and (10831009).
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Zhou, Y.Y., Yang, X.Q. Augmented Lagrangian functions for constrained optimization problems. J Glob Optim 52, 95–108 (2012). https://doi.org/10.1007/s10898-011-9688-z
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DOI: https://doi.org/10.1007/s10898-011-9688-z