Convergence rates for the variable, the multiplier, and the pair in SQP methods
Tapia, Richard A.
Doctor of Philosophy
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 $q\sb1$ factor. Finally we present a condition that guarantees $q$-superlinear convergence in $x$, $\lambda$ and ($x,\lambda$).