Nonlinear unconstrained optimization methods: A review

In this review paper, we report recent results in the study of nonlinear unconstrained optimization methods, such as nonlinear penalty function method and nonlinear Lagrangian method. One important feature of this line of research is that unconstrained optimization problems may be nonlinear in the cost function of the original constraint problem. Results such as zero duality gaps, exact penalization, and the existence of nonlinear Lagrange multipliers are reviewed.