On an exact penalty function method for semi-infinite programming problems

In this paper, we study a new exact and smooth penalty function for semi-infinite programming problems with continuous inequality constraints. Through this exact penalty function, we can transform a semi-infinite programming problem into an unconstrained optimization problem. We find that, under some reasonable conditions when the penalty parameter is sufficiently large, the local minimizer of this penalty function is the local minimizer of the primal problem. Moreover, under some mild assumptions, the local exactness property is explored. The numerical results demonstrate that it is an effective and promising approach for solving constrained semi-infinite programming problems.