Polyak Minorant Method for Convex Optimization

Nikhil Devanathan () and Stephen Boyd ()
Additional contact information
Nikhil Devanathan: Stanford University
Stephen Boyd: Stanford University

Journal of Optimization Theory and Applications, 2024, vol. 203, issue 3, No 7, 2263-2282

Abstract: Abstract In 1963 Boris Polyak suggested a particular step size for gradient descent methods, now known as the Polyak step size, that he later adapted to subgradient methods. The Polyak step size requires knowledge of the optimal value of the minimization problem, which is a strong assumption but one that holds for several important problems. In this paper we extend Polyak’s method to handle constraints and, as a generalization of subgradients, general minorants, which are convex functions that tightly lower bound the objective and constraint functions. We refer to this algorithm as the Polyak Minorant Method (PMM). It is closely related to cutting-plane and bundle methods.

Keywords: Convex optimization; First-order methods; Cutting-plane methods; Bundle methods; 49M20; 49M37; 90C25; 90C55 (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/s10957-024-02412-7 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:203:y:2024:i:3:d:10.1007_s10957-024-02412-7

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

DOI: 10.1007/s10957-024-02412-7

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 ().