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In this paper, a modified simple penalty function is proposed for a constrained nonlinear programming problem by augmenting the dimension of the program with a variable that controls the weight of the penalty terms. This penalty function enjoys improved smoothness. Under mild conditions, it can be proved to be exact in the sense that local minimizers of the original constrained problem are precisely the local minimizers of the associated penalty problem. MSC: 47H20, 35K55, 90C30. © 2012 Bingzhuang and Wenling; licensee Springer.

A modified exact smooth penalty function for nonlinear constrained optimization