Convergence Rates for the Variable, the Multiplier, and the Pair in SQP Methods

: This work investigates relationships among the convergence rates for the variable x, for the multiplier lambda and for the pair (x, lambda) in SQP methods for equality constrained optimization. Key contributions are: if the convergence in (x, lambda) and also in x is q-superlinear, then the convergence in lambda is either q-superlinear or q-sublinear with unbounded q1 factor, and if the convergence in (x, lambda) is q-superlinear, then the convergence in x is at least two-step q-superlinear. It is noted that a theorem of Fontecilla, Steihaug and Tapia leads to a characterization result which is potentially more useful than the Boggs-Tolle-Wang characterization. Finally, two different conditions that guarantee q-superlinear convergence in x, lambda and (x, lambda) for an SQP method are derived.