The Inexact Cyclic Block Proximal Gradient Method and Properties of Inexact Proximal Maps

Leandro Farias Maia (), David Huckleberry Gutman () and Ryan Christopher Hughes ()
Additional contact information
Leandro Farias Maia: Texas A &M University
David Huckleberry Gutman: Texas A &M University
Ryan Christopher Hughes: U.S. Patent and Trademark Office

Journal of Optimization Theory and Applications, 2024, vol. 201, issue 2, No 7, 668-698

Abstract: Abstract This paper expands the cyclic block proximal gradient method for block separable composite minimization by allowing for inexactly computed gradients and pre-conditioned proximal maps. The resultant algorithm, the inexact cyclic block proximal gradient (I-CBPG) method, shares the same convergence rate as its exactly computed analogue provided the allowable errors decrease sufficiently quickly or are pre-selected to be sufficiently small. We provide numerical experiments that showcase the practical computational advantage of I-CBPG for certain fixed tolerances of approximation error and for a dynamically decreasing error tolerance regime in particular. Our experimental results indicate that cyclic methods with dynamically decreasing error tolerance regimes can actually outpace their randomized siblings with fixed error tolerance regimes. We establish a tight relationship between inexact pre-conditioned proximal map evaluations and $$\delta $$ δ -subgradients in our $$(\delta ,B)$$ ( δ , B ) -Second Prox theorem. This theorem forms the foundation of our convergence analysis and enables us to show that inexact gradient computations can be subsumed within a single unifying framework.

Keywords: Coordinate descent; Proximal gradient; Deterministic convergence rates; Block separable; Nonsmooth optimization (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-024-02404-7 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:joptap:v:201:y:2024:i:2:d:10.1007_s10957-024-02404-7

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-024-02404-7

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

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