Convergence rates for the variable, the multiplier, and the pair in SQP methods

[摘要] 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 $qsb1$ factor. Finally we present a condition that guarantees $q$-superlinear convergence in $x$, $lambda$ and ($x,lambda$).

[发布机构] Rice University