2000 journal article

Superlinear convergence and implicit filtering


By: T. Choi* & C. Kelley*

author keywords: noisy optimization; implicit filtering; BFGS algorithm; superlinear convergence
TL;DR: This paper shows 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. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

1999 journal article

Estimates for the Nash-Sofer preconditioner for the reduced Hessian for some elliptic variational inequalities


By: T. Choi* & C. Kelley*

author keywords: preconditioners; reduced Hessian; elliptic variational inequalities
TL;DR: A class of examples is presented to show how the quality of the Nash--Sofer preconditioner can be directly estimated and one consequence 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, then the condition number of the reduced Hessian can be lowered. (via Semantic Scholar)
UN Sustainable Development Goal Categories
10. Reduced Inequalities (OpenAlex)
Source: Web Of Science
Added: August 6, 2018

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