1. DERIVATIVE-FREE OPTIMIZATION OF NOISY FUNCTIONS VIA QUASI-NEWTON METHODS.
- Author
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BERAHAS, ALBERT S., BYRD, RICHARD H., and NOCEDAL, JORGE
- Subjects
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QUASI-Newton methods , *FINITE difference method , *NUMERICAL analysis , *SCALABILITY , *NEWTON-Raphson method - Abstract
This paper presents a finite-difference quasi-Newton method for the minimization of noisy functions. The method takes advantage of the scalability and power of BFGS updating, and employs an adaptive procedure for choosing the differencing interval h based on the noise estimation techniques of Hamming [Introduction to Applied Numerical Analysis, Courier Corporation, North Chelmsford, MA, 2012] and Mor\'e and Wild [SIAM J. Sci. Comput., 33 (2011), pp. 1292--1314]. This noise estimation procedure and the selection of h are inexpensive but not always accurate, and to prevent failures the algorithm incorporates a recovery mechanism that takes appropriate action in the case when the line-search procedure is unable to produce an acceptable point. A novel convergence analysis is presented that considers the effect of a noisy line-search procedure. Numerical experiments comparing the method to a function interpolating trust-region method are presented. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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