Convergence Rates for the Variable, the Multiplier, and the Pair in SQP Methods
In this work we consider 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. We show that if the convergence in (x,lambda)is q-superlinear, then the convergence in x is at least two-step q-superlinear. Moreover, 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 q1factor. We extend the Boggs-Tolle-Wang characterization of q-superlinear convergence in x to the case where it is known that the convergence in (x,lambda) is q-superlinear. Finally we present a condition that guarantees q-superlinear convergence in x, lambda and (x,lambda) for an SQP method.
Citable link to this pagehttps://hdl.handle.net/1911/101654
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