An augmented memoryless BFGS method based on a modified secant equation with application to compressed sensing

Aminifard, Zohre; Babaie-Kafaki, Saman; Ghafoori, Saeide

doi:10.1016/j.apnum.2021.05.002

Cited by 6 publications

(2 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In another part of our numerical experiments, we evaluate performance of the diagonally scaled memoryless BFGS methods for solving the compressed sensing problem which essentially deals with sparse solutions of an underdetermined system of linear equations. Details of the problem model as well as the smoothing technique can be found in [7]. The initial process starts from the origin.…”

Section: K+1mentioning

confidence: 99%

See 1 more Smart Citation

Diagonally scaled memoryless quasi–Newton methods with application to compressed sensing

Aminifard

Babaie-Kafaki

2023

JIMO

Self Cite

View full text Add to dashboard Cite

<p style='text-indent:20px;'>Memoryless quasi–Newton updating formulas of BFGS (Broyden–Fletcher–Goldfarb–Shanno) and DFP (Davidon–Fletcher–Powell) are scaled using well-structured diagonal matrices. In the scaling approach, diagonal elements as well as eigenvalues of the scaled memoryless quasi–Newton updating formulas play significant roles. Convergence analysis of the given diagonally scaled quasi–Newton methods is discussed. At last, performance of the methods is numerically tested on a set of CUTEr problems as well as the compressed sensing problem.</p>

show abstract

Section: K+1mentioning

confidence: 99%

“…To assess the restoration performance qualitatively, we report relative error (Rel-Err) [7] of the recovered signal (in percent). Figures 6-10 show the results for different choices of the sampling matrix [28].…”

Section: K+1mentioning

confidence: 99%