Newton-type methods for constrained optimization with nonregular constraints

The most important classes of Newton-type methods for solving constrained optimization problems are discussed. These are the sequential quadratic programming methods, active set methods, and semismooth Newton methods for Karush–Kuhn–Tucker systems. The emphasis is placed on the behavior of these methods and their special modifications in the case where assumptions concerning constraint qualifications are relaxed or altogether dropped. Applications to optimization problems with complementarity constraints are examined.