Item Details

abstract

The computational power growth nowadays does not match the demands of the datasize growth. Efficient algorithms are needed in almost every large numerical optimization task. Decades ago Broyden, Fletcher, Goldfarb, and Shanno discovered the Broyden{Fletcher{Goldfarb{Shanno algorithm based on Newton’s algorithm. This algorithm latter was modified as limited-memory BFGS algorithm that has a prominent record in computational efficiency. Limited-memory BFGS can have different forms based on the compact formulas of the BFGS. In this thesis, two different compact BFGS formulas, David Ek and Anders Forsgren (2020) and Byrd, R.H., Nocedal, J. & Schnabel, R.B. (1994), are compared in terms of computational costs under different situations. The compact BFGS formula from David Ek and Anders Forsgren (2020) is converted into limited-memory BFGS. Numerical experiments are conducted based on this limited-memory BFGS. According to the experiment results and analysis, we find that this limited-memory BFGS does not guarantee positive definite property as other limited-memory BFGS normally do. To solve this problem more research in combining line search and trust region methods are needed.

subject

contributor

Xia, Jinxin (author)

Erway, Jennifer (committee chair)

Berenhaut, Kenneth (committee member)

Erhardt , Rob (committee member)

date

2021-06-03T08:36:07Z (accessioned)

2022-06-02T08:30:11Z (available)

2021 (issued)

degree

Mathematics and Statistics (discipline)

embargo

2022-06-02 (terms)

identifier

http://hdl.handle.net/10339/98808 (uri)

language

en (iso)

publisher

Wake Forest University

title

COMPARING COMPACT QUASI-NEWTON FORMULATIONS

type

Thesis