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Superlinear Convergence And Implicit Filtering (1999)
| Content Provider | CiteSeerX |
|---|---|
| Author | Choi, T. D. Kelley, C. T. |
| Abstract | . 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 1. Introduction. In this paper we examine the local and global convergence behavior of the combination of the BFGS [4], [20], [17], [23] quasi-Newton method with the implicit filtering algorithm. The resulting method is intended to minimize smooth functions that are perturbed with low-amplitude noise. Our results, which extend those of [5], [15], and [6], show that if the amplitude of the noise decays ... |
| File Format | |
| Journal | SIAM J. OPTIM |
| Journal | SIAM J. Optim |
| Publisher Date | 1999-01-01 |
| Access Restriction | Open |
| Subject Keyword | Known Theory Low-amplitude Noise Optimal Point Noisy Optimization Implicit Filtering Noise Decay Implicit Filtering Algorithm Objective Function Decay Superlinear Convergence Am Subject Classification Superlinear Convergence Superlinearly Convergent Iteration Bfgs Algorithm Global Convergence Behavior Quasi-newton Method Bfgs Quasi-newton Update Good Performance Smooth Function Noise-free Case Partial Explanation |
| Content Type | Text |
| Resource Type | Article |
