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