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Conjugate Gradient Methods with Inexact Searches
Abstract
Conjugate gradient methods are iterative methods for finding the minimizer of a scalar function f(x) of a vector variable x which do not update an approximation to the inverse Hessian matrix. This paper examines the effects of inexact linear searches on the methods and shows how the traditional Fletcher-Reeves and Polak-Ribiere algorithm may be modified in a form discovered by Perry to a sequence which can be interpreted as a memorytess BFGS algorithm. This algorithm may then be scaled optimally in the sense of Oren and Spedicalo. This scaling can be combined with Beale restarts and Powell's restart criterion. Computational results will show that this new method substantially outperforms known conjugate gradient methods on a wide class of problems.
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Citations
Cited by
Backpropagation through time: what it does and how to do it
Werbos, P. J. (1990) · Proceedings of the IEEE · doi:10.1109/5.58337 · Cited by 4,879
First- and Second-Order Methods for Learning: Between Steepest Descent and Newton's Method
Battiti, R. (1992) · Neural Computation · doi:10.1162/neco.1992.4.2.141 · Cited by 1,193
Metadata
- Authors
- Shanno, D. F.
- Venue
- Mathematics of Operations Research
- Published
- 1978-08
- Volume
- 3
- Issue
- 3
- Pages
- 244-256
- ISSN
- 0364-765X (ISSN-L)
- 1526-5471
- OpenAlex
- W2122565324
- Cited by
- 480
- References
- 0
- FWCI
- 8.80
- Type
- journal article
- Language
- en
- Open access
- closed
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- Shanno, D. F. (1978). Conjugate Gradient Methods with Inexact Searches. Mathematics of Operations Research. https://doi.org/10.1287/moor.3.3.244
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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