Exact penalty functions for constrained minimization problems via regularized gap function for variational inequalities

By using the regularized gap function for variational inequalities, we introduce a new penalty function P-alpha(x) for the problem of minimizing a twice continuously differentiable function in a closed convex subset of the n-dimensional space R-n. Under certain assumptions, it is shown that any stationary point of the penalty function P-alpha( x) satisfies the first-order optimality condition of the original constrained minimization problem, and any local ( or global) minimizer of P-alpha(x) on R-n is a locally ( or globally) optimal solution of the original optimization problem.