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

摘要

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 R~n. 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 R~n is a locally (or globally) optimal solution of the original optimization problem.