@article{choi_kelley_2000, title={Superlinear convergence and implicit filtering}, volume={10}, ISSN={["1052-6234"]}, DOI={10.1137/S1052623499354096}, abstractNote={In this paper we show how the implicit filtering algorithm can be coupled with the BFGS quasi-Newton update to obtain a superlinearly convergent iteration if the noise in the objective function decays sufficiently rapidly as the optimal point is approached. In this way we give insight into the observations of good performance in practice of quasi-Newton methods when they are coupled with implicit filtering. We also report on numerical experiments that show how an implementation of implicit filtering that exploits these new results can improve the performance of the algorithm.}, number={4}, journal={SIAM JOURNAL ON OPTIMIZATION}, author={Choi, TD and Kelley, CT}, year={2000}, month={Jun}, pages={1149–1162} }
 @article{choi_kelley_1999, title={Estimates for the Nash-Sofer preconditioner for the reduced Hessian for some elliptic variational inequalities}, volume={9}, ISSN={["1052-6234"]}, DOI={10.1137/S1052623497323364}, abstractNote={The purpose of this paper is to present a class of examples to show how the quality of the Nash--Sofer preconditioner can be directly estimated. This class of examples includes certain discretized elliptic variational inequalities. We use sparsity and locality properties of discretizations of elliptic operators and smoothing properties of their inverses to estimate the quality of the preconditioner. One consequence of our results is that if the Hessian is the five-point discretization of a certain type of strongly elliptic operator with homogeneous Dirichlet boundary conditions on an $n \times n$ mesh and the preconditioner is a fast Poisson solver for that discretization, then the condition number of the reduced Hessian can be lowered from O(n2) to O(n ln(n)). We illustrate these theoretical results with calculations.}, number={2}, journal={SIAM JOURNAL ON OPTIMIZATION}, author={Choi, TD and Kelley, CT}, year={1999}, month={Apr}, pages={327–341} }