Two Classes of Smooth Objective Penalty Functions for Constrained Problems

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This research aims at solving constrained problems by providing two classes of objective penalty functions which respectively approach to a class of exact penalty functions smoothly. Meanwhile, the authors present two algorithms based on the two objective penalty functions, and give the conclusion that all of the cluster points of the two sequences generated by the two algorithms are the optimal points of the original problem. Furthermore, this article discusses that both of the two penalty functions are of well-condition. Finally, the authors report numerical results to show the applicability of the two presented algorithms.