On the convergence of the iterates of proximal gradient algorithm with extrapolation for convex nonsmooth minimization problems

Bo Wen () and Xiaoping Xue ()
Additional contact information
Bo Wen: Hebei University of Technology
Xiaoping Xue: Harbin Institute of Technology

Journal of Global Optimization, 2019, vol. 75, issue 3, No 7, 767-787

Abstract: Abstract In this paper, we consider the proximal gradient algorithm with extrapolation for solving a class of convex nonsmooth minimization problems. We show that for a large class of extrapolation parameters including the extrapolation parameters chosen in FISTA (Beck and Teboulle in SIAM J Imaging Sci 2:183–202, 2009), the successive changes of iterates go to 0. Moreover, based on the Łojasiewicz inequality, we establish the global convergence of iterates generated by the proximal gradient algorithm with extrapolation with an additional assumption on the extrapolation coefficients. The assumption is general enough to allow the threshold of the extrapolation coefficients to be 1. In particular, we prove the length of the iterates is finite. Finally, we perform numerical experiments on the least squares problems with $$\ell _1$$ ℓ 1 regularization to illustrate our theoretical results.

Keywords: Convex minimization; Proximal gradient algorithm; Extrapolation; Łojasiewicz inequality; Convergence (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10898-019-00789-8 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jglopt:v:75:y:2019:i:3:d:10.1007_s10898-019-00789-8

Ordering information: This journal article can be ordered from
http://www.springer. ... search/journal/10898

DOI: 10.1007/s10898-019-00789-8

Access Statistics for this article

Journal of Global Optimization is currently edited by Sergiy Butenko

More articles in Journal of Global Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().