Derivation of Coordinate Descent Algorithms from Optimal Control Theory

Isaac M. Ross ()
Additional contact information
Isaac M. Ross: Naval Postgraduate School

SN Operations Research Forum, 2023, vol. 4, issue 2, 1-11

Abstract: Abstract Recently, it was posited that disparate optimization algorithms may be coalesced in terms of a central source emanating from optimal control theory. Here we further this proposition by showing how coordinate descent algorithms may be derived from this emerging new principle. In particular, we show that basic coordinate descent algorithms can be derived using a maximum principle and a collection of max functions as “control” Lyapunov functions. The convergence of the resulting coordinate descent algorithms is thus connected to the controlled dissipation of their corresponding Lyapunov functions. The operational metric for the search vector in all cases is given by the Hessian of the convex objective function.

Keywords: Coordinate descent; Nonsmooth control Lyapunov functions; Machine learning; Singular optimal control theory; Convex optimization (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s43069-023-00215-6 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:snopef:v:4:y:2023:i:2:d:10.1007_s43069-023-00215-6

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/43069

DOI: 10.1007/s43069-023-00215-6

Access Statistics for this article

SN Operations Research Forum is currently edited by Marco Lübbecke

More articles in SN Operations Research Forum from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().