Back to Search Start Over

Polyak Minorant Method for Convex Optimization.

Authors :
Devanathan, Nikhil
Boyd, Stephen
Source :
Journal of Optimization Theory & Applications. Dec2024, Vol. 203 Issue 3, p2263-2282. 20p.
Publication Year :
2024

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. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00223239
Volume :
203
Issue :
3
Database :
Academic Search Index
Journal :
Journal of Optimization Theory & Applications
Publication Type :
Academic Journal
Accession number :
181515969
Full Text :
https://doi.org/10.1007/s10957-024-02412-7