Pith. sign in

REVIEW 1 cited by

Polyak Minorant Method for Convex Optimization

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2310.07922 v4 pith:OID4PCF2 submitted 2023-10-11 math.OC

classification math.OC
keywords polyakmethodmethodssizestepconvexfunctionsminorant
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original 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.

Discussion (0). Sign in to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On the construction of a gradient method of quadratic optimization, optimal from the point of view of minimizing the distance to the exact solution

    math.OC 2025-06 conditional novelty 4.0 of 10

    An m-moment minimum error method is constructed for quadratic optimization in Hilbert space, with proved convergence, optimality among Krylov methods, and numerical tests on Helmholtz, heat, and thermoacoustics invers...

Pith tools