All previously known results concerned with attraction of Newton-type iterations for optimality systems to critical Lagrange multipliers were a posteriori by nature: they were showing that in case of convergence, the dual limit is in a sense unlikely to be noncritical. This paper suggests the ﬁrst a priori result in this direction, showing that critical multipliers actually serve as attractors: for a fully quadratic optimization problem with equality constraints, under certain reasonable assumptions we establish actual local convergence to a critical multiplier starting from a “dense” set around the given critical multiplier. This is an important step forward in understanding the attraction phenomenon.
Moscow State University, OR Department, 2012
View Attraction of Newton method to critical Lagrange multipliers: fully quadratic case