Text

A Proximal Bundle Variant with Optimal Iteration-Complexity for a Large Range of Prox Stepsizes

This paper presents a proximal bundle variant, namely, the relaxed proximal bundle (RPB) method, for solving convex nonsmooth composite optimization problems. Like other proximal bundle variants, RPB solves a sequence of prox bundle subproblems whose objective functions are regularized composite cutting-plane models. Moreover, RPB uses a novel condition to decide whether to perform a serious or null iteration which does not necessarily yield a function value decrease. Optimal iteration-complexity bounds for RPB are established for a large range of prox stepsizes, in both convex and strongly convex settings. To the best of our knowledge, this is the first time that a proximal bundle variant is shown to be optimal for a large range of prox stepsizes. Finally, iteration-complexity results for RPB to obtain iterates satisfying practical termination criteria, rather than near optimal solutions, are also derived.

Ketersediaan

Informasi Detail

Judul Seri

SIAM JOURNAL ON OPTIMIZATION; Vol.31 No.4 October-December 2021

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 2955-2986

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

ITERATION-COMPLEXITY
NONSMOOTH COMPOSITE OPTIMIZATION
PROXIMAL BUNDLE METHOD
OPTIMAL COMPLEXITY BOUND

Info Detail Spesifik

https://doi.org/10.1137/20M1327513

Pernyataan Tanggungjawab

Jiaming Liang, Renato D. C. Monteiro

Versi lain/terkait

Lampiran Berkas

Komentar