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In this paper, we present a new exact and smooth penalty function for nonlinear programming problems by adding only one variable no matter how many constraints. Through the smooth and exact penalty function, we can transform the nonlinear programming problems into unconstrained optimization models. We demonstrate that under some general conditions, when the penalty parameter σ > 0 is sufficiently large, the minimizer of this penalty function is the minimizer of the primal problem, which can be obtained after finite iterations. Alternatively, under some mild assumptions, sufficient conditions are derived for the local exactness property. The numerical results demonstrate that the new penalty function is reasonable and is an effective approach for solving a class of nonlinear programming problem with equality and inequality constraints.

A new exact penalty function method for nonlinear programming problems