Superlinear Convergence and Implicit Filtering

In this note 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. We show how known theory for the noise-free case can be extended and thereby provide a partial explanation for the good performance of quasi-Newton methods when coupled with implicit filtering. Key words. noisy optimization, implicit filtering, BFGS algorithm, superlinear convergence AMS subject classifications. 65K05, 65K10, 90C30

• Type: Journal
• Year: 2000
• Where: SIAMJO
• Authors: T. D. Choi, C. T. Kelley
• Keywords: Implicit Filtering, Implicit Filtering Algorithm, SIAMJO 2000, Superlinearly Convergent Iteration