Attraction of Newton method to critical Lagrange multipliers: fully quadratic case

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.